19 lanes · 239 modules — 0% complete.

Layer 1 - Foundation · due 2026-07-01 · 40h · critical

Proof writing from scratch. Direct proof, contradiction, contrapositive, induction, sets, functions, relations. Everything above this depends on proof fluency.

Source: Velleman ↗

• All chapters 1-7
• Write full proofs for all four main techniques
• Error-log every attempt that fails on first try

backups: MIT 6.042J Mathematics for Computer Science (Fall 2010) — Visual proof companion — watch the lecture that matches the Velleman chapter you're stuck on. Saved alongside the textbook for the moments where Velleman's text-only explanation feels thin. · MIT 18.200 Principles of Discrete Applied Mathematics (Spring 2024) — Proving Theorems notes (PDF) — 12-page handout you read ONCE in Week 1 as the writeup style template. Calibrates what 'clean proof on paper' looks like in MIT's voice.

Layer 1 - Foundation · due 2026-07-31 · 60h · critical

ODEs are the language MIT SCH UROP work needs (phase planes, stability, linear systems, Laplace transform, qualitative analysis). Follow MIT 18.03 OCW Spring 2010 (Mattuck) since it has 33 video lectures pinned to a clean problem-set schedule. Text companion: Edwards-Penney 'Differential Equations and Boundary Value Problems' Ch. 1-5, 7. Pair MIT ES.1803 (Jeremy Orloff Spring 2024) as the cleaner modular alternative if Mattuck's pacing is too fast.

Source: Mattuck (lectures) / Edwards-Penney (text) ↗

• MIT 18.03 Mattuck lectures 1-33 paired with the matching Edwards-Penney sections
• Edwards-Penney problems: every 4th problem in each section you cover
• Hand-sketch the phase plane for every 2x2 linear system you meet
• One Laplace-transform proof rewritten from scratch by the end of July
• Backup if Mattuck moves too fast: switch to MIT ES.1803 (Orloff) Spring 2024 — same syllabus, slower pacing, cleaner notes

• Mattuck L1-L7 + Edwards-Penney Ch.1 (first-order ODEs, separation, integrating factors, linear, models)2026-06-12
• Mattuck L8-L10 + Edwards-Penney Ch.2 (numerical methods, autonomous, equilibrium, stability)2026-06-19
• Mattuck L11-L16 + Edwards-Penney Ch.3 (second-order linear constant-coeff, undetermined coeffs, variation of parameters, harmonic oscillator)2026-07-03
• Mattuck L19-L21 + Edwards-Penney Ch.7 (Laplace transform, convolution, step/impulse forcing)2026-07-12
• Mattuck L22-L26 + Edwards-Penney Ch.5 (2x2 first-order linear systems, eigenvalues, phase portraits, fundamental matrix)2026-07-22
• Mattuck L27-L33 (nonlinear autonomous systems, Lyapunov stability, limit cycles, numerical solvers) — required before SCH UROP main work2026-07-31

Layer 1 - Foundation · due 2026-08-15 · 60h · critical

Structural linear algebra without determinants first. Vector spaces, linear maps, eigenvalues, inner product spaces, spectral theorem.

Source: Axler ↗

• Chapters 1-9 fully
• Slow down on chapter 5 (eigenvectors)
• Prove every major theorem in your own words before reading Axler's proof

• Ch. 1-3 vector spaces and maps2026-07-15
• Ch. 4-6 polynomials, eigenvalues, inner products2026-08-01
• Ch. 7-9 operators and spectral theorem2026-08-15

backups: Sheldon Axler's own video lectures (Linear Algebra Done Right, 3rd ed playlist) — Author-led companion. Watch the matching video AFTER reading the chapter, BEFORE doing exercises. The author's intuition resolves the abstract definition problem better than any reader. · MIT 18.06 Linear Algebra (Strang, Spring 2010) — Concrete/computational counterpart when Axler's abstraction feels unmotivated. Strang teaches column space and matrix viewpoint that Axler deliberately skips first. Cherry-pick lectures, don't watch all 35.

Layer 1 - Foundation · due 2026-08-31 · 35h · high

CMU Dynamic Logic channel teaches Platzer's textbook over 22 lessons paired with the lfcps.org chapters. Hybrid systems, differential dynamic logic (dL), KeYmaera X proof tool. Pairs with the ODE work because verification = WHEN the ODE solution stays in a safe set. Watch alongside MIT 18.03 so the ODE concepts you just learned get a logic/verification layer on top. Useful for MIT SCH UROP touching anything autonomous, robotic, or safety-critical.

Source: Andre Platzer (CMU) ↗

• Watch the 22-lesson YouTube playlist in order; each video pairs with one chapter at lfcps.org
• Work through the chapter exercises before advancing to the next video
• Install KeYmaera X (https://keymaerax.org) by week 2 and verify the cruise-control example
• Sketch one autonomous-vehicle invariant in dL by Aug 15

• Lessons 1-3 + lfcps.org Ch.1-3 (hybrid programs, ODEs+domains, choice & control)2026-07-15
• Lessons 4-7 + lfcps.org Ch.4-7 (safety/contracts, dynamic axioms, truth/proof, control loops & invariants)2026-08-05
• Lessons 8-13 + lfcps.org Ch.8-13 (events, reactions, differential invariants, ghosts, proof theory)2026-08-22
• KeYmaera X cruise-control verification proved end-to-end2026-08-31

Layer 2 - Core Analysis · due 2026-12-15 · 25h · medium

Gentler companion to Rudin. Use it aggressively in 2026 to keep Rudin chapters 1-4 moving before the first Putnam. Not a substitute - a bridge.

Source: Abbott ↗

• Read only the sections matching the Rudin chapter currently blocking you
• Use Abbott to repair definitions, examples, and intuition
• Return to Rudin exercises immediately after the repair pass

Layer 2 - Core Analysis · due 2027-03-15 · 120h · critical

Baby Rudin. Sequences, topology on R, continuity, differentiation, Riemann-Stieltjes integration. The proof-maturity engine for everything above. This cannot sit 11 months out if the goal is to outrun the standard curriculum.

Source: Rudin ↗

• Checkpoint: chapters 1-2 by September 2026
• Checkpoint: chapters 3-4 by December 2026 for the first Putnam rewrite cycle
• Checkpoint: chapters 5-6 by January 2027 and chapters 7-9 by March 2027
• Every bold exercise in each chapter; use Abbott only to unblock, not to replace Rudin

• Ch. 1-2 definitions, sets, metric topology2026-09-01
• Ch. 3-4 sequences, series, continuity2026-12-01
• Ch. 5-6 differentiation and Riemann-Stieltjes2027-01-31
• Ch. 7-9 functions, special functions, multivariable2027-03-15

backups: MIT 18.100B Real Analysis (Spring 2025) — 23 official video lectures pinned to Rudin's syllabus. Use as the lecture spine that runs alongside reading — one lecture per Rudin chapter where they align. · Bright Side of Mathematics — Real Analysis — Short chunked videos (5-15 min each) on every Rudin concept. Use when one specific theorem in Rudin breaks and a 10-minute walkthrough would unblock you. Don't binge — search by topic.

Layer 3 - Algebra, Complex, ODE, Fourier · due 2027-05-15 · 65h · high

Holomorphic functions, Cauchy's theorem, Laurent series, conformal maps, residues. Putnam integral shortcuts and the bridge to harmonic analysis.

Source: Stein & Shakarchi (Princeton Lectures, Vol. 2) ↗

• Chapters 1-8 core
• Every exercise in chapters 1-5
• Log every problem where a complex viewpoint shortens a proof

Layer 3 - Algebra, Complex, ODE, Fourier · due 2027-06-15 · 100h · high

Groups, rings, fields, modules. Makes hard Putnam number-theory proofs feel like pattern recognition. Required for algebraic geometry, algebraic number theory, and qualifying exams.

Source: Dummit & Foote ↗

• Parts I-IV (groups and rings) required
• Part V (fields/Galois theory) for algebraic depth
• 20+ exercises per chapter - do not skip computation problems

Layer 3 - Algebra, Complex, ODE, Fourier · due 2027-06-15 · 45h · medium

Classical ODE techniques: separation of variables, integrating factors, series solutions, Laplace transforms, systems. Dover edition. Dense with every technique Arnold's geometric approach assumes you can already execute. Use as the computational twin to Arnold.

Source: Tenenbaum & Pollard ↗

• Chapters 1-6 (classical techniques) alongside Arnold's geometric exposition
• Laplace transform section pairs with Stein Fourier later
• Every technique in this book should be executable in under 10 minutes before moving to L4

Layer 3 - Algebra, Complex, ODE, Fourier · due 2027-08-15 · 55h · high

ODE through the lens of geometry and flows. Phase spaces, stability, and the geometric view that makes PDE intuition click.

Source: Arnold ↗

• Chapters 1-5 required
• Read alongside Strogatz for the applied intuition side
• Every proof should be understood geometrically, not just algebraically

Layer 3 - Algebra, Complex, ODE, Fourier · due 2027-08-15 · 55h · high

Fourier series, convergence theorems, Fourier transform, applications. Prerequisite for Folland and Evans PDE.

Source: Stein & Shakarchi (Princeton Lectures, Vol. 1) ↗

• Chapters 1-5 core
• Link to Rudin chapter 11 for Lebesgue perspective
• Bridge to Evans PDE and Folland chapter 8

Layer 3 - Algebra, Complex, ODE, Fourier · due 2027-09-01 · 45h · low

[Tier 3 - optional] ODE intuition via phase portraits, fixed points, bifurcations. Useful alongside Arnold for intuition but cuttable. Cross-goal test: Putnam Low, PhD qualifying Low (Arnold already covers ODE), Interview Low. Pick up only if Arnold needs supplementing and time permits.

Source: Strogatz ↗

• Chapters 1-6 required
• Chapter 8 (Lorenz) as enrichment
• Read alongside Arnold; Strogatz explains what Arnold assumes

Layer 3 - Algebra, Complex, ODE, Fourier · due 2028-01-15 · 65h · critical

Completes the Princeton Lectures sequence. Vol. 1 (Fourier) and Vol. 2 (Complex) are already in the plan - skipping Vol. 3 is architecturally incoherent. Covers Lp spaces, distributions, and Hilbert space theory. The bridge between Stein Fourier and Folland measure theory. Tier 1.

Source: Stein & Shakarchi (Princeton Lectures, Vol. 3) ↗

• Chapters 1-6 core (measure theory, integration, Lp spaces, Hilbert spaces)
• Chapter 3 (Lp spaces) connects directly to Folland chapters 6-7
• Read immediately after completing Stein Fourier - the sequence is designed to flow continuously

Layer 4 - Graduate Core · due 2027-11-01 · 80h · high

Bridge from Rudin to Folland. Lebesgue measure and integration, Lp spaces. Read before Folland to reduce the jump.

Source: Royden ↗

• Parts I-III core
• Focus on chapter 3 (Lebesgue integration) - this is where Rudin ends and Folland begins
• Use as a stepping stone, not a final destination

Layer 4 - Graduate Core · due 2028-01-15 · 50h · low

[Tier 3 - optional] Undergraduate differential geometry. Lee Smooth Manifolds is more modern and more complete - Lee is the right choice for this plan. Cross-goal test: Putnam Low, PhD Low, Interview Low. Pick up only if Lee's abstraction feels unmotivated and time permits.

Source: do Carmo ↗

• Chapters 1-4 fully (curves, regular surfaces, Gauss map, intrinsic geometry)
• Every problem in chapters 3-4 builds the intuition Lee assumes
• Only open if Lee's Chapter 1 feels unmotivated - Lee's appendix covers most of this

Layer 4 - Graduate Core · due 2028-02-15 · 40h · low

[Tier 3 - optional] Classical PDE techniques. Redundant with Strauss which already covers undergraduate PDE techniques at the level this plan needs. Cross-goal test: Putnam Low, PhD Low (Strauss covers it), Interview Low. Only open if Strauss is insufficient for a specific computation.

Source: Farlow ↗

• Parts I-III (separation of variables, Fourier, transforms)
• Run Farlow's computational techniques alongside Strauss's theoretical exposition
• Only use when Strauss is too terse on a specific technique - otherwise Strauss is sufficient

Layer 4 - Graduate Core · due 2028-04-01 · 65h · high

Sufficient statistics, likelihood, estimation, hypothesis testing, Bayesian basics. Pairs with Billingsley + Durrett for a complete probability+statistics layer.

Source: Casella & Berger ↗

• Chapters 1-10 core
• All main theorems with full proofs
• Essential for PhD qualifying exams in statistics

Layer 4 - Graduate Core · due 2028-04-01 · 120h · critical

Graduate measure theory standard. Measure theory, Lp spaces, Radon-Nikodym, functional analysis intro. PhD first-year standard.

Source: Folland ↗

• Chapters 1-7 required
• Chapter 9 (Fourier) integrates with Stein-Fourier
• The hardest single book in the stack - budget 3+ months

Layer 4 - Graduate Core · due 2028-05-01 · 60h · high

[CONDITIONAL on December 2027 Putnam] Ahlfors is the graduate complex analysis standard at Harvard, MIT, and Chicago specifically. If top 100 Putnam 2027: add this to Bucket 4. If below top 200: drop it, Stein Complex is sufficient for the realistic program targets. See the December 2027 Putnam milestone decision prompt.

Source: Ahlfors ↗

• Chapters 1-6 core (complex differentiation through conformal mappings)
• Chapter 5 (Riemann surfaces) distinguishes Ahlfors from Stein at the qualifying exam level
• Only open after Stein Complex is fully complete and top 100 Putnam 2027 is confirmed

Layer 4 - Graduate Core · due 2028-05-01 · 65h · low

[Tier 3 - optional] Graduate analytic number theory: arithmetic functions, Dirichlet series, zeta function. Only if going deep into analytic number theory as a research direction. Cross-goal test: Putnam Low (Hardy & Wright + Dummit covers Putnam NT), PhD Low (not tested on applied math qualifying), Interview Low. Hardy and Wright plus Dummit is sufficient for every stated goal.

Source: Apostol ↗

• Chapters 1-8 core (arithmetic functions through Dirichlet series)
• Only open if analytic number theory becomes a specific research direction
• Hardy and Wright covers competition NT; Dummit covers algebraic NT - Apostol fills the analytic bridge only if needed

Layer 4 - Graduate Core · due 2028-05-01 · 80h · critical

Measure-theoretic probability: convergence theorems, CLT, martingales, Brownian motion intro. Foundation for Shreve. British-style treatment, strong on weak convergence.

Source: Billingsley ↗

• Chapters 1-25 required
• Must have Folland chapters 1-4 stable first
• Second half (ch 26+) only if quant track is active

Layer 4 - Graduate Core · due 2028-05-01 · 55h · high

Undergraduate PDE: wave, heat, Laplace equations, boundary value problems. Entry point before Evans graduate PDE.

Source: Strauss ↗

• Chapters 1-10 core
• Do before Evans - Strauss removes the shock of Evans' abstraction
• Work every problem in chapters 1-4 (classical equations)

Layer 4 - Graduate Core · due 2028-05-15 · 70h · low

[Tier 3 - optional] The classical applied math toolkit in one volume. Holmes covers the specific perturbation gap more efficiently. Logan is broader but overlaps with Holmes, Strauss, and Evans. Cross-goal test: Putnam Low, PhD Low (Holmes is sufficient for qualifying), Interview Low. Lower priority than every other book in this layer.

Source: Logan ↗

• Only open if Holmes is insufficient for a specific topic lookup
• Chapter 3 (perturbation) previews Holmes - read Holmes instead
• Use as a reference only, not a cover-to-cover read

Layer 4 - Graduate Core · due 2028-06-01 · 75h · high

Point-set topology: metric spaces, connectedness, compactness, metrization. Required for functional analysis and real analysis depth.

Source: Munkres ↗

• Chapters 1-5 required
• Part II chapters 9-11 for algebraic topology intro
• Every exercise in chapters 3-5

Layer 4 - Graduate Core · due 2028-07-01 · 30h · high

~200 pages, Cambridge standard. Fills the martingale gap between Billingsley and Shreve and makes the transition smooth. Low cost, high value. Read after the core Billingsley pass - Williams is elegant where Billingsley is encyclopedic.

Source: Williams ↗

• Parts I-III in full - the book is short enough to cover completely
• Chapter 12 (martingales) is the key chapter - read slowly
• Connect directly to Shreve II Chapter 3 (Brownian motion and martingales)

Layer 4 - Graduate Core · due 2028-08-01 · 90h · medium

Smooth manifolds, vector fields, differential forms, integration on manifolds, Stokes' theorem. Needed for geometric mechanics and applied differential geometry.

Source: Lee ↗

• Chapters 1-16 core
• Chapter 9 (integral curves and flows) connects to Arnold ODE
• Requires Munkres topology + do Carmo geometry as foundation

Layer 5 - Advanced Applied · due 2028-07-01 · 75h · high

Convex sets, duality, LP/QP/SOCP, KKT conditions. Free online from Stanford. Core for quant finance, ML, and optimization research.

Source: Boyd & Vandenberghe ↗

• Chapters 1-9 core
• Use Stanford EE364a problem sets alongside
• Duality and applications chapters are the interview-relevant half

Layer 5 - Advanced Applied · due 2028-07-01 · 60h · high

Regular and singular perturbation, matched asymptotic expansions, WKB, multiple-scale analysis, boundary layers. Core applied math curriculum that MIT, Chicago, Princeton, and Stanford all expect - and no other book in the stack covers it. This is one of the clearest gaps for a serious applied math PhD applicant.

Source: Holmes ↗

• Chapters 1-5 required (regular, singular, WKB, multiple scales, boundary layers)
• Chapter 4 (boundary layers) is the hardest and most important for PDE intuition
• Verify every asymptotic expansion numerically - error in O-notation is easy to miss

Layer 5 - Advanced Applied · due 2028-07-15 · 80h · high

Banach and Hilbert spaces, bounded operators, spectral theory, compact operators. Required for serious PDE and operator theory work.

Source: Kreyszig ↗

• Chapters 1-7 core
• Chapter 9 (compact operators) for PDE prep
• Every theorem statement rewritten in your own words before the exercises

Layer 5 - Advanced Applied · due 2028-08-01 · 60h · medium

The algebraic number theory text that PhD programs use — the complement to Hardy & Wright (analytic) and Apostol (analytic NT). Ireland & Rosen brings the modern algebraic perspective: Gauss sums, quadratic reciprocity proved three different ways, Dirichlet's theorem on primes in progressions, Dirichlet series and L-functions, cyclotomic fields, Fermat curves, and an introduction to elliptic curves. MIT, Princeton, and Chicago number theory and algebraic geometry adjacent programs expect fluency with this material. It also feeds Putnam directly: Gauss sums and quadratic residues appear in hard Putnam NT problems (B-5/B-6 level) in ways that Hardy & Wright alone does not prepare you for. Prerequisites: Dummit (abstract algebra) solid, Burton (elementary NT) and Apostol (analytic NT) done.

Source: Ireland & Rosen ↗

• Chapters 1-4: integers, unique factorization, congruences, Gauss's lemma — bridge from Burton to algebraic NT
• Chapters 5-9: quadratic reciprocity (three proofs), Gauss sums, primitive roots — the Putnam-relevant core
• Chapters 12-14: algebraic number theory, Dirichlet's theorem, L-functions — the PhD prerequisite layer
• Chapters 18-19: elliptic curves introduction — know what they are and why Wiles needed them

Layer 5 - Advanced Applied · due 2028-08-01 · 90h · critical

Brownian motion, Ito's lemma, SDEs, Black-Scholes, risk-neutral pricing, term structure models. Core quant finance mathematics.

Source: Shreve ↗

• Chapters 1-6 required
• Chapter 4 (stochastic calculus) is the hardest - go slowly
• Requires Billingsley chapters 1-20 for the measure-theoretic foundation

backups: MIT 18.642 Topics in Mathematics with Applications in Finance (Fall 2024) — MIT's applied finance math course — 25 lectures pinned to the exact Shreve II topics. The lectures cover what the book proves with the practitioner motivation Shreve assumes you have. Use the matching lectures BEFORE each Shreve chapter to make the math feel grounded. · MIT 18.650 Statistics for Applications (Fall 2016) — Statistical inference companion when Casella & Berger feels too theoretical. Use selected lectures only — the regression and hypothesis-testing units are the relevant ones for quant interviews.

Layer 5 - Advanced Applied · due 2028-09-01 · 55h · low

[Tier 3 - optional] Ergodic theory: measure-preserving transformations, ergodic theorems, entropy. Cross-goal test: Putnam Low (never appears), PhD Low (not tested on applied math qualifying), Interview Low. No path to any of the three stated goals. After graduation only if research interest develops.

Source: Walters ↗

• Chapters 1-5 core (measure-preserving systems through ergodic theorems)
• Read after Billingsley and Durrett are stable - only if research interest demands it
• Only relevant if dynamical systems or statistical mechanics becomes a specific research direction

Layer 5 - Advanced Applied · due 2028-10-01 · 65h · critical

The path Kreyszig to Evans assumes Sobolev fluency that Kreyszig does not actually build. Brezis covers functional analysis and Sobolev spaces together - exactly what Evans assumes. Every serious applied math program uses it. Tier 1. Survivable cut: second cut after Vershynin if Bucket 5 slips (Kreyszig alone gets you to Evans with more struggle but it works).

Source: Brezis ↗

• Chapters 1-9 core (Lp spaces through Sobolev spaces)
• Chapter 8 (Sobolev spaces) is the essential chapter - it unlocks Evans chapters 5-6
• Read after Kreyszig is stable - Brezis assumes Banach/Hilbert space fluency

Layer 5 - Advanced Applied · due 2028-10-01 · 100h · high

Graduate PDE: classical equations, weak solutions, Sobolev spaces. Read Strauss and Farlow first to remove the abstraction shock.

Source: Evans ↗

• Parts I and II required
• Chapter 5 (Sobolev spaces) requires Folland chapters 1-4
• PhD-level reading - pace carefully

Layer 5 - Graduate Problem Sets · starts 2028-10-01 · due 2028-12-15 · 35h · high

Application-season math depth through actual qualifier problems. No application writing, no admin, no vague signal work: only analysis problems from graduate qualifying archives tied back to Folland, Brezis, Evans, and Rudin.

Source: Berkeley / Chicago / MIT qualifier archives ↗

• Solve 20 real analysis / functional analysis qualifier problems
• For every miss, trace the missing theorem to Folland, Brezis, Evans, or Rudin
• Keep only clean full solutions or clearly labeled partial attempts

Layer 5 - Advanced Applied · due 2029-06-01 · 50h · low

[Tier 3 - optional] Free online. Concentration inequalities, random matrices, subgaussian tails. Valuable for modern applied math research, but enrichment rather than qualifying material. Defer unless a specific research project needs it before applications.

Source: Vershynin ↗

• Chapters 1-5 core (basic inequalities through random matrices)
• Chapter 3 (random vectors) connects directly to high-dimensional geometry
• Read after Billingsley and Durrett - requires measure-theoretic probability fluency

Layer 6 - Graduate Problem Sets · starts 2029-01-01 · due 2029-03-31 · 45h · high

Senior probability depth through problems only: convergence, martingales, Brownian motion, stopping times, Ito calculus, and pricing exercises.

Source: Billingsley, Williams, Shreve ↗

• Billingsley: convergence and weak convergence problems
• Williams: martingale and stopping-time problems
• Shreve II: Brownian motion, Ito formula, and risk-neutral pricing exercises

Layer 6 - Graduate Problem Sets · starts 2029-01-01 · due 2029-03-31 · 55h · high

Senior analysis depth through exercises only. This is a selected hard-problem pass across measure theory, functional analysis, Sobolev spaces, and PDE.

Source: Folland, Brezis, Evans ↗

• Folland: selected problems from measure, integration, Lp, product measures, Radon-Nikodym
• Brezis: selected Banach/Hilbert/Sobolev problems
• Evans: selected weak derivative, Sobolev, elliptic PDE problems

Layer 6 - PhD Level · due 2029-06-01 · 90h · medium

[PhD Year 1] The standard US PhD probability qualifying exam text at MIT, Chicago, Stanford, and Princeton. Before graduation, Billingsley plus Williams is enough; Durrett becomes the deeper first-year probability pass.

Source: Durrett ↗

• Chapters 1-7 required (measure theory through Brownian motion)
• Chapter 5 (martingales) is the most important chapter for quant finance prep
• Use after the pre-graduation probability spine is stable

Layer 6 - PhD Level · due 2029-06-01 · 45h · medium

[PhD Year 1] Variational principles, optimal control foundations, Hamilton-Jacobi equation. PhD programs teach this - arrive with the book and complete it in graduate year 1. Deferred from pre-graduation lanes because Kirk is also deferred and the connection is indirect enough that it is not load-bearing before December 2028.

Source: Gelfand & Fomin ↗

• All 8 chapters - the book is short enough to read fully
• Chapter 6 (canonical equations) connects Hamiltonian mechanics to HJB
• Engage at graduate seminar level in PhD year 1 rather than cramming before December 2028

Layer 6 - PhD Level · due 2029-06-01 · 65h · medium

[PhD Year 1] Pontryagin minimum principle, dynamic programming, Hamilton-Jacobi-Bellman equation. Same reasoning as Gelfand & Fomin - PhD programs teach this, arrive with the book, engage at graduate seminar level. Deferred from Bucket 5 to keep the pre-graduation hour count executable.

Source: Kirk ↗

• Chapters 1-5 core (variational through HJB)
• Read Gelfand & Fomin first - Kirk assumes that variational intuition
• Connect HJB to Shreve II Chapter 4 and Evans Chapter 4 (second-order elliptic)

Layer 6 - PhD Level · due 2029-06-01 · 65h · medium

[PhD Year 1] SVD, QR, iterative methods, eigenvalue algorithms. MAT 385 covers undergraduate numerical analysis. Trefethen is PhD year 1 material - arrive knowing the theory, engage with Trefethen at graduate seminar depth. Deferred from pre-graduation lanes to keep Bucket 5 executable.

Source: Trefethen & Bau ↗

• Lectures 1-35 in order
• Implement 5+ algorithms from scratch (QR, Gram-Schmidt, power method, CG)
• Compare theoretical bounds against actual floating-point behavior

Layer 6 - PhD Level · due 2029-06-01 · 65h · medium

ARIMA models, spectral analysis, GARCH, state-space models. The standard reference for financial time series and quantitative econometrics. Every quant research role that involves volatility modeling or return predictability draws on this material.

Source: Brockwell & Davis ↗

• Chapters 1-8 core (stationary processes, ARMA, prediction, spectral analysis)
• Chapter 8 (ARCH/GARCH) is the most interview-relevant for finance roles
• Read alongside Shreve II and ESL - connects stochastic calculus, statistical learning, and empirical finance

Layer 6 - PhD Level · due 2029-06-01 · 55h · low

[Tier 3 - conditional] Information theory: entropy, mutual information, channel capacity. Only if quantum/information theory research develops in the PhD. Cross-goal test: Putnam Low, PhD Low, Interview Low. Not load-bearing for any stated goal. PhD year 1 if interest develops, otherwise skip.

Source: Cover & Thomas ↗

• Chapters 1-8 core
• Chapter 2 (entropy) slowly - every inequality deserves its proof
• Only open if research direction specifically requires information theory

Layer 6 - PhD Level · due 2029-06-01 · 100h · medium

Advanced real and complex analysis at the PhD qualifier level. Hp spaces, Banach algebra, harmonic analysis. Bridges Folland and advanced functional analysis.

Source: Rudin (Papa Rudin) ↗

• Parts I-III core
• Read after Folland is fully stable
• Use in PhD year 1 alongside graduate coursework

Layer 6 - Graduate Problem Sets · starts 2029-04-01 · due 2029-06-15 · 60h · high

Final-quarter applied math problem work: reproduce computations, examples, and small numerical experiments from serious sources.

Source: Trefethen / Boyd / Evans / Shreve examples ↗

• Reproduce 3 numerical linear algebra examples from Trefethen & Bau
• Reproduce 2 convex optimization examples from Boyd
• Reproduce 2 PDE or stochastic-calculus examples from Evans or Shreve II

Layer 6 - Graduate Problem Sets · starts 2029-04-01 · due 2029-06-15 · 45h · high

Final undergraduate bridge through actual first-year graduate problems. Use public qualifier and course problem sets only.

Source: MIT / Berkeley / Chicago / Stanford archives ↗

• Solve 10 analysis qualifier problems
• Solve 8 probability or stochastic process qualifier problems
• Solve 6 applied math / PDE / numerical analysis problems

Layer 7 - PhD Year 1 · due 2029-04-01 · 90h · high

The canonical PhD-level stochastic analysis text. Shreve's Finance volumes (I and II) are excellent for building intuition and connecting to pricing — but Karatzas & Shreve is what MIT, Princeton, and NYU Courant PhD students study in their first year when specializing in stochastic analysis. The difference: Shreve assumes you want to reach Black-Scholes; K&S assumes you want to understand the full mathematical structure of continuous-time processes. K&S derives Brownian motion from first principles (Wiener measure, path-space regularity), builds the filtration theory carefully, proves the martingale representation theorem at full generality, and treats stochastic control and optimal stopping rigorously via the dynamic programming principle. If your PhD specialization is stochastic analysis or mathematical finance, this is your dissertation-language text.

Source: Karatzas & Shreve ↗

• Ch. 1-2: Brownian motion construction and path properties — compare carefully with Shreve II Ch. 1, the precision level is different
• Ch. 3: stochastic integration — the full measure-theoretic treatment; work every proof, not just the statements
• Ch. 4: Brownian motion and partial differential equations — the Feynman-Kac connection in full generality, essential for stochastic PDE work
• Ch. 5: stochastic differential equations — existence and uniqueness proofs, strong vs. weak solutions
• Ch. 6: P. Lévy's theory of Brownian local time — optional but connects to modern research in random media

Layer 7 - PhD Year 1 · due 2029-06-15 · 80h · high

The definitive reference for continuous-time martingale theory. Where Karatzas & Shreve is the pedagogy text, Revuz & Yor is the reference that every stochastic analysis researcher has on their desk — it contains results that appear nowhere else in book form. Covers: local time and its applications, the Tanaka formula, Ray-Knight theorems, Bessel processes, excursion theory, and the structure of continuous semimartingales. The Tanaka formula and local time are prerequisites for understanding any modern research in stochastic analysis and stochastic PDEs (SPDEs). If you are targeting a research group in stochastic analysis at MIT (Mossel, Sheffield) or NYU Courant (Vanden-Eijnden, Lin), this is the book your advisor's papers cite on page 1.

Source: Revuz & Yor ↗

• Ch. 1-3: martingales, Brownian motion, and the stochastic integral — build on K&S, fill in the gaps
• Ch. 4-6: Ito's formula, local time, Tanaka formula — local time is the hardest concept, revisit three times
• Ch. 8: Bessel processes — appear in random matrix theory and diffusion literature; know what they are
• Ch. 12: excursion theory — Itô's excursion theory is the foundation of modern stochastic analysis research; this is PhD research language
• Strategy: use as a reference alongside K&S, not as a cover-to-cover read; identify 3-4 chapters most relevant to your advisor's papers and master those

Putnam Prep - Meta · due 2026-09-01 · 20h · high

The foundational text on mathematical heuristics. Read once at the start, revisit quarterly. Shapes how you approach any problem.

Source: Polya ↗

• Read Part I and II actively
• Build a personal heuristic checklist from this book
• Revisit one heuristic per week during Putnam practice

Putnam Prep - Meta · due 2026-10-01 · 45h · high

Meta-level attacking: tactics, strategies, and habits. Use to sharpen your approach before the harder archive grind.

Source: Zeitz ↗

• Parts I and II fully
• Build a personal heuristic checklist
• Apply at least one tactic from each chapter to a real Putnam problem

Putnam Prep - Primary · due 2026-11-15 · 70h · critical

The early systematic Putnam backbone. In this tracker, the goal is a first pass through proof methods plus the early algebra, number theory, combinatorics, and analysis chapters before the first Putnam. The detailed ongoing grind lives in the Putnam Prep site.

Source: Gelca & Andreescu ↗

• Chapter 1 (proof methods) first and fully
• Before December 2026: proof methods, algebra basics, number theory basics, combinatorics basics, and selected analysis problems
• After each math book checkpoint, revisit matching PnB problems and rewrite old misses

• Proof methods first pass2026-08-15
• Algebra + number theory first pass2026-09-30
• Combinatorics + selected analysis first pass2026-11-15

Putnam Prep - Foundations · due 2026-12-01 · 30h · medium

Competition counting and probability foundations. Combinatorial proofs, generating functions intro, expected value.

Source: AoPS / David Patrick ↗

• Chapters 1-11 core
• Build a counting triggers page: bijection, complement, IE, stars and bars
• Pair with Putnam and Beyond combinatorics chapter

Putnam Prep - Foundations · due 2026-12-01 · 30h · medium

Competition number theory foundations. Divisibility, modular arithmetic, primes, Diophantine equations at the right problem-solving level.

Source: AoPS / Mathew Crawford ↗

• Chapters 1-10 core
• Every exercise - these are short but build the right reflexes
• Pair with Putnam and Beyond number theory chapter

Putnam Prep - Foundations · due 2026-12-01 · 35h · medium

Classical undergraduate number theory: divisibility, primes, congruences, quadratic reciprocity, arithmetic functions. More complete theoretical arc than the AoPS NT book. Read alongside or after AoPS NT before opening Hardy & Wright.

Source: Burton ↗

• Chapters 1-8 core (divisibility through primitive roots)
• Every proof should be reproduced without reference before moving on
• Pairs with AoPS NT: AoPS for problem reflexes, Burton for theorem proofs

Putnam Prep - 28-week roadmap (Dec 5 exam) · due 2026-12-05 · 200h · critical

The real week-by-week training lives in the Putnam Prep roadmap (this site's #roadmap view) - gated ladders, the AI proof checker, enrichment quotas, the Slot keep-warm gate. This tracker item just anchors WHERE you should be by each date so the Putnam grind stays synced with URAP + coursework prep. Summer = the most free time = bank the most volume NOW; fall (classes + URAP tail) must be peak/conversion, not first exposure. Top-200 = cleanly finishing A1/A2/B1/B2.

Source: Putnam Prep roadmap ↗

• Use the #roadmap gated ladders + AI checker daily - that is the volume engine
• Summer (free time): clear Gear-1 Scout and most of Gear-2 Cement
• Fall (classes + URAP tail): Convert slot mastery + Peak mocks, NOT first exposure
• Keep the Slot keep-warm gate live every week so A1/A2/B1/B2 stay automatic

• Gear-1 SCOUT done (wk 1-6): proof language + AIME ramp + full topic scout2026-07-05
• Gear-2 CEMENT through ~wk 14: analysis, algebra, combinatorics, NT + advanced gates (LTE, SOS, the 3 methods, abstract algebra)2026-08-31
• Gear-2 CEMENT complete (wk 7-16): + linear algebra, geometry, USAMO bridge2026-09-13
• Gear-3 CONVERT (wk 17-24): A1/A2/B1/B2 slot mastery + verification intensive2026-11-08
• PEAK (wk 25-28): full mocks + taper -> EXAM Saturday Dec 52026-12-05

backups: Putnam Prep roadmap (this site - #roadmap) — The actual gated week-by-week training, AI proof checker, enrichment quotas. · Kedlaya Putnam archive — Official problems + solutions the roadmap pulls from.

Putnam Prep - December 2026 Attempt · due 2026-12-05 · 30h · critical

The first-attempt self-study finish lane. This card freezes new materials before exam week; mocks and archive usage stay in the Putnam Prep site.

Source: Books, handouts, and topic sheets ↗

• Nov 25 onward: no new self-study materials for this attempt
• Finish chapter/topic sheets before the review buffer
• Use Dec 1-4 for theorem recall, trigger sheets, and cleaned notes
• Putnam Prep owns timed work, archive problems, and mocks

• Material freeze starts: no new 2026 self-study books2026-11-25
• Review sheet packet drafted2026-11-30
• Topic recall and theorem trigger sheets cleaned2026-12-02
• Exam-week review packet complete2026-12-04

Putnam Prep - Meta · due 2027-01-15 · 40h · high

The systematic companion to Zeitz. Where Zeitz teaches the philosophy of problem solving, Larson gives you chapter-by-chapter technique drills organized exactly as Putnam problems are categorized: induction, pigeonhole, parity, counting, algebra, calculus, analytic geometry, inequalities, number theory. Specifically recommended by the Illinois Putnam seminar, Toronto Putnam seminar, and Stanford Putnam page as the best Putnam technique reference. Chapters map one-to-one to Putnam topic families — this is the book you return to after each autopsy to fill a named gap. Start after Zeitz so the philosophical layer is established before the technique layer.

Source: Loren Larson ↗

• Chapter 1 (induction): work every example, then apply the technique to 5 PnB induction problems
• Chapter 2 (pigeonhole) and Chapter 3 (parity/invariants): the most Putnam-dense chapters
• Chapter 6 (calculus techniques): differentiating under the integral, Stolz-Cesàro — things Rudin doesn't teach explicitly
• After Putnam 2026 autopsy: open the chapter matching your weakest classified topic and work it systematically

Putnam Prep - Postmortem · due 2027-02-01 · 15h · high

Research Experience for Undergraduates applications typically close January 15 - February 15. Summer 2027 is sophomore summer — the right window to target a computational math, applied math, or probability REU. A strong first Putnam showing, proof-writing ability from Abbott and Axler, and a faculty recommendation letter are the main inputs. Strong programs: NSF math REUs at Michigan, SMALL at Williams, Summer@ICERM, UChicago math, and any program with stochastic processes or combinatorics focus.

Source: NSF REU programs — math.NSF.gov, mathprograms.org ↗

• By December 15: finalize list of 8-12 target REU programs and their individual deadlines via mathprograms.org
• By January 1: personal statement draft — lead with Putnam attempt, proof-writing background, and a specific math area you want to explore
• By January 15: submit first application; prioritize early-deadline programs
• Letters: 2 math faculty who have seen your proof writing in office hours, exams, or a reading course

Putnam Prep - Postmortem · due 2027-02-15 · 30h · high

Post-first-attempt repair block. Score gains for 2027 come from classifying misses, rewriting reachable problems, and turning vague weaknesses into named topics.

Source: Putnam archive + personal error log ↗

• Classify every 2026 miss: knowledge gap, recognition gap, algebra slip, time triage, or proof-writing gap
• Rewrite at least 12 old misses in clean contest-proof form
• Produce a 2027 top-100 weakness map with the next book/problem source attached to each weakness

Putnam Prep - Gap Filling · due 2027-03-01 · 35h · high

Classical Euclidean competition geometry. Fills the main gap in the plan - competition geometry is not covered by the analysis/algebra track.

Source: Coxeter & Greitzer ↗

• Chapters 1-5 fully
• Every problem in chapters 2 and 3 (circles and transformations)
• Log all geometry problems from past Putnams and solve with techniques from this book

Putnam Prep - Gap Filling · due 2027-04-01 · 40h · high

Inequalities at elite depth. Makes inequality problems a real family instead of one-off tricks. Essential for hard Putnam algebra/analysis slots.

Source: Steele ↗

• All 12 chapters
• Write your own proof of every named inequality before reading Steele's version
• Build a personal inequality toolkit page from this book

Putnam Prep - Gap Filling · due 2027-04-01 · 30h · high

Free online. The single most powerful Putnam combinatorics technique spelled out from scratch. Generating functions for sequences, coefficient extraction, recurrence solving. Every serious Putnam student knows this book.

Source: Wilf ↗

• Chapters 1-3 fully (the core technique)
• For every recurrence you encounter elsewhere, attempt the GF treatment first
• Pairs with the combinatorics chapter of Putnam and Beyond

Putnam Prep - Gap Filling · due 2027-06-01 · 40h · medium

Topic-specific gap-filling with competition-style problems across three major Putnam areas.

Source: Andreescu ↗

• Work by topic section matching current weak areas
• Only mark a problem done after writing a clean polished proof
• Cross-reference with Putnam and Beyond for technique consistency

Putnam Prep - Meta · due 2027-06-01 · 50h · medium

The bridge book that IMO-pipeline students use to see graduate mathematics before formally studying it. Free 800-page PDF. Covers groups, rings, modules, representation theory, topology, complex analysis, algebraic geometry, category theory, and more — all at an olympiad pace, meaning concise, proof-driven, and example-heavy. Not a replacement for Dummit, Rudin, or Ahlfors — it's the map you read so the individual books feel coherent. The gap between olympiad math and graduate math is partly psychological: everything feels disconnected until you see how it all fits. The Napkin fixes this. Read it non-linearly: use chapters that match your current book reading as a second perspective.

Source: Evan Chen (free PDF — web.evanchen.cc/napkin.html) ↗

• Read the groups/rings chapters alongside Dummit — Evan's exposition is faster and fills the intuition gaps
• Read the topology chapters alongside Munkres — the Napkin's categorical perspective makes Munkres's point-set definitions feel purposeful
• Read the complex analysis chapter alongside Ahlfors — different emphasis, same theorems, very useful
• Don't try to master it: use it as a guided tour, not a textbook. The goal is recognizing patterns across areas.

Putnam Prep - Gap Filling · due 2027-08-01 · 60h · high

Graduate-level combinatorics: permutations, set partitions, generating functions, Ramsey theory, extremal combinatorics, graph theory. More systematic and deeper than any other combinatorics book in the plan. Combinatorics is the highest-volume Putnam topic - this is the right investment.

Source: Bona ↗

• Chapters 1-12 in order (the core combinatorial structures)
• Chapter 9 (Ramsey theory) and Chapter 12 (extremal) are the highest Putnam ROI
• Every chapter has exercises graded by difficulty - solve at least the first two tiers before moving on

Putnam Prep - Postmortem · due 2027-08-15 · 5h · critical

This decision point must be made in August 2027, not January 2028 when the deadlines overlap. The conflict: quant firm offers (Jane Street, Citadel) come in October-November 2027. REU applications for Summer 2028 are due January-February 2028. If you accept a quant internship for Summer 2028, you lose the second REU window. If you target a second REU, you may be deferring the quant path by a year. Both paths are legitimate — but the answer depends on whether your goal is quant trading (internship wins) or applied math PhD (second REU wins). Make this decision explicitly before recruiting season opens, so you're not reactively applying to everything.

Source: Personal — faculty conversations, firm research ↗

• By July 2027: have one honest conversation with a math professor about your research potential and PhD fit
• By August 2027: decide primary target — quant career path or PhD path — and plan accordingly
• Quant path: focus Fall 2027 fully on firm applications and interview prep
• PhD path: apply to REUs for Summer 2028 in January, defer or decline quant internship offers

Putnam Prep - December 2027 Attempt · due 2027-12-05 · 30h · critical

Second attempt finish lane. After November 15, no new books opened for the 2027 exam. The full problem-solving stack is deeper now — the job is timed archive work, clean proof production, and score calibration for a meaningful result. The 2027 attempt is the primary target for a real score.

Source: Putnam Prep site + archive ↗

• Nov 15 onward: taper begins — switch entirely to timed work from archive
• Run two full timed A/B mini-sets per week in the final three weeks
• Rewrite every reachable miss from the 2026 autopsy map in clean proof form
• Exam-week rule: no new theory, only review, sleep, and confidence

• Taper starts: freeze new books for 2027 attempt2027-11-15
• Timed mini-mock 1 plus rewrite2027-11-21
• Timed mini-mock 2 plus weak-family repair2027-11-28
• Exam-week review packet complete2027-12-04

Putnam Prep - Top 100 Target · due 2028-01-01 · 70h · high

The classical number theory text. Primes, Diophantine approximation, quadratic forms, Waring's problem, Riemann zeta. Covers the number-theoretic depth behind the hardest Putnam NT problems that Burton and AoPS cannot reach.

Source: Hardy & Wright ↗

• Chapters 1-10 core (primes through quadratic residues)
• Chapter 22 (Riemann zeta) as enrichment after Apostol is underway
• Work alongside Apostol - Hardy & Wright gives intuition, Apostol gives technique

Putnam Prep - Postmortem · due 2028-02-15 · high

The Goldwater Scholarship is the premier undergraduate research award in STEM — $10,000 per year, and a credential that PhD programs recognize immediately. Applications go through your institution's internal nomination process (typically November) and are submitted by February. The research essays require a named faculty mentor and a concrete research project or ongoing REU output. This is why the Summer 2027 REU research output matters directly — it feeds the Goldwater essay.

Source: Goldwater Foundation — goldwaterscholarship.org ↗

• By November 2027: internal Goldwater nomination submitted with department endorsement
• Research essay: describe the REU project clearly, name your faculty mentor, state the open question you addressed
• Three recommendation letters: ideally REU supervisor plus two math faculty who have seen proof work
• GPA must be strong — keep all math courses at A level

• Internal nomination submitted through institution2027-11-15
• Research and future plans essays finalized2028-01-15
• Full application submitted2028-02-15

Putnam Prep - Top 100 Target · due 2028-06-01 · 50h · medium

Harder problem sets for the top 100 target. Step up from standard Putnam difficulty toward olympiad-style problems.

Source: Andreescu & Feng ↗

• Work problems by topic after each matching Putnam and Beyond section
• Only attempt after Putnam and Beyond chapters feel solid
• Log every unsolved problem with the obstacle clearly named

Putnam Prep - Top 100 Target · due 2028-08-01 · 60h · medium

Elegant problems at the boundary of competition and real mathematics. For building the instinct that distinguishes top 100 solvers.

Source: Andreescu & Dospinescu ↗

• Read the solution chapters fully even for problems you solved
• Each problem should produce one transferable technique or insight
• Pair with the matching self-study book layer for maximum transfer

Putnam Prep - Top 100 Target · due 2028-10-01 · 50h · medium

Graduate qualifying exam problems overlapping with the hardest Putnams. Exposes you to PhD-level problem formats before you arrive.

Source: De Souza & Silva ↗

• Work after Layer 4 math is at least 60% complete
• Use as a cross-check: if a problem type is unsolvable, it names a gap in the math stack
• Track which qualifying exam area each problem tests

Putnam Prep - Final Attempt · due 2028-10-15 · 60h · high

Required for HYPSM applied math PhD applications. The Math GRE is administered in September and October — the October sitting is the last before December PhD application deadlines. It covers calculus (50%), algebra (25%), and additional topics including real analysis, topology, complex analysis, probability, and combinatorics (25%). A student who has completed Rudin, Dummit, Folland, and Blitzstein should score in the 90th percentile with 60–80 hours of focused prep. The test rewards breadth and speed over depth — many problems are solved in under 90 seconds.

Source: ETS practice exams + Putnam/Berkeley Problems ↗

• By July 2028: take ETS practice exam cold to establish baseline
• August 2028: systematic review of calculus topics (most problems are calculus) — Paul's Notes is the right reference
• September 2028: two full timed practice exams under real conditions; review every miss
• Register for the October sitting — this is the last sitting before most PhD deadlines
• Target: 90th percentile (scaled score ~900). With the math stack from this plan, 95th percentile is realistic.

• Cold practice exam: baseline score established2028-07-15
• Calculus review complete (50% of exam)2028-08-15
• Full timed practice exam 12028-09-07
• Full timed practice exam 2 plus registration confirmed2028-09-28

Putnam Prep - Final Attempt · due 2028-11-01 · high

Senior year is the single most consequential fellowship window of your undergraduate career. NSF GRFP (mid-October), Hertz Fellowship (October), Rhodes Scholarship (October), Gates Cambridge (October), and Fulbright US Student (November) all close within six weeks of each other. Each requires completely distinct essays — NSF wants research potential and broader impacts; Hertz wants scientific vision and independence; Rhodes wants leadership and character; Gates Cambridge wants commitment to improving lives; Fulbright wants cultural exchange and project feasibility (strongest if you have a named host institution abroad). Start drafting in August. You need 5-6 faculty letters coordinated across all applications. The Goldwater in February 2028 is the rehearsal. Fulbright is viable if you have a clear international research project — pair with a Cambridge or ETH Zurich professor during the REU networking period.

Source: NSF, Hertz Foundation, Rhodes Trust, Gates Cambridge, US Fulbright Program ↗

• August 2028: draft NSF personal statement and research statement — show 2 years of research trajectory
• September 2028: draft Rhodes personal statement — the character and leadership angle, very different tone from NSF
• September 2028: Hertz application — most technically demanding, requires scientific vision statement
• September-October 2028: Fulbright — identify host institution and faculty contact by August; project statement is the core document
• October 1-15: submit NSF, Hertz, Rhodes, and Gates Cambridge; do not let Putnam prep crowd this window
• November: Fulbright submission deadline — stagger deliberately after the October cluster
• Faculty letters: REU supervisor writes the research letter; math faculty write the technical letters; a third faculty writes the leadership letter for Rhodes and Fulbright

• All five personal statements in first-draft form (include Fulbright project statement)2028-09-01
• All faculty letter requests sent with materials2028-09-07
• NSF GRFP submitted2028-10-15
• Hertz, Rhodes, and Gates Cambridge submitted2028-10-15
• Fulbright US Student application submitted2028-11-01

Putnam Prep - Final Attempt · starts 2028-10-01 · due 2028-12-05 · 40h · high

Final undergraduate Putnam problem block: hard archive problems and full written repairs.

Source: Putnam archive + Kedlaya archive ↗

• Solve 20 A3/B3/A4/B4 archive problems by topic
• Rewrite every miss into a complete proof before moving on
• Use Kedlaya archive solutions only after a serious attempt

Putnam Prep - Graduate Problem Sets · starts 2029-01-01 · due 2029-03-15 · 60h · high

Senior proof maturity through problems only. Use Putnam archive problems, Berkeley Problems in Mathematics, and graduate seminar sheets.

Source: Putnam archive / Berkeley Problems / seminar sheets ↗

• Solve 12 high-quality problems across algebra, analysis, combinatorics, probability, and geometry
• Prefer problems whose solutions require a theorem from the self-study stack
• Keep clean written solutions because the writing exposes fake understanding

Putnam Prep - Top 100 Target · due 2029-06-01 · 60h · low

[Tier 3 - optional] Using probability to prove existence in combinatorics. Beautiful and powerful, but not part of the default Putnam path unless the core combinatorics lane is already ahead of schedule.

Source: Alon & Spencer ↗

• Chapters 1-6 core (the basic method through the Lovasz Local Lemma)
• For every problem: write down the probability space before anything else
• Pairs with Bona and Putnam and Beyond combinatorics

Mental Math - Estimation · due 2026-08-01 · 15h · high

Free MIT PDF. Fermi estimation, order-of-magnitude reasoning, dimensional analysis. Jane Street and quant trading interviews test this directly - 'how many ping pong balls fit in a 747' type reasoning under pressure. The one book that targets the exact cognitive skill separating a strong mathematician from a strong quant in a live interview. Short enough to read in a week.

Source: Mahajan (MIT) ↗

• Chapter 1 (dimensional analysis) and Chapter 3 (lumping) are the highest ROI
• Every estimation: write down the answer before calculating, calibrate
• After each chapter: find a real estimation question from Glassdoor quant reports and apply the technique

Mental Math - Arithmetic · due 2026-08-01 · 20h · high

Fast arithmetic: multiplication, squaring, division shortcuts. Arithmetic should never slow you down on Zetamac or in a quant interview.

Source: Benjamin ↗

• Read and practice chapters 1-4 intensively
• Run Zetamac daily for 5 minutes after reading each chapter
• Target: 3-digit multiplication in under 10 seconds

Mental Math - Arithmetic · due 2026-10-01 · 15h · medium

Extension of mental arithmetic techniques into advanced calculations. Complements Secrets of Mental Math.

Source: Benjamin ↗

• Use as a follow-on after Secrets is comfortable
• Focus on techniques not covered in Secrets
• Integrate with daily Zetamac practice

Mental Math - Fast Probability · due 2026-12-01 · 20h · high

50 classic probability puzzles with full solutions. The fastest-ROI probability book in the entire plan. Every quant interviewer uses problems from this book.

Source: Mosteller ↗

• Work all 50 problems cold before reading solutions
• Classify each problem: conditioning, expectation, symmetry, or direct count
• Re-solve any problem you got wrong after 1 week

Mental Math - Fast Probability · due 2027-01-01 · 45h · high

Probability at the right level of rigor for fast problem solving. Story proofs, conditional probability, distributions, transforms.

Source: Blitzstein & Hwang ↗

• Chapters 1-10 core
• Every story proof should become a template you can apply instantly
• Pairs with Mosteller for speed and Billingsley for rigor

Mental Math - Fast Probability · due 2027-06-01 · 35h · medium

Graduate-level probability problems for speed and depth. Harder than Mosteller, deeper than Blitzstein.

Source: Shiryaev ↗

• Work chapters matching current Billingsley progress
• Use as a stretch source - not every problem needs to be solved
• Log any technique you couldn't reproduce from memory

Quant Interview - Probability · due 2026-12-01 · 20h · critical

Shared with Lane 3. Every quant interviewer uses problems from this book. Complete before any serious interview prep.

Source: Mosteller ↗

• Work all 50 problems cold before reading solutions
• This is the single highest-ROI book for quant probability interviews
• Re-solve every problem you got wrong after 1 week

Quant Interview - Core · due 2027-05-01 · 40h · critical

The primary quant interview prep text. Brain teasers, probability, statistics, finance, C++ questions. This belongs in the Autumn 2027 recruiting window, not late 2028, so sophomore/junior internship screens are not surprised by basic quant categories.

Source: Xinfeng Zhou (Green Book) ↗

• Work all sections in order after Mosteller and Shreve I are stable
• Use it for sophomore recruiting readiness by October 2027
• Every problem should be solved without reference before checking the answer

Quant Interview - Core · due 2027-06-30 · 30h · high

Quantitative finance interview questions from decades of Wall Street recruiting. Probability puzzles, options intuition, brainteasers. This is the timed replay layer after Green Book, useful before winter screens and junior internship follow-ups.

Source: Timothy Crack ↗

• Parts I-III fully
• Pair with Green Book - use Heard for the finance/derivatives questions
• Time yourself on every problem and track your improvement

Quant Interview - Stochastic Calc · due 2027-07-01 · 55h · high

Discrete stochastic calculus, risk-neutral pricing, martingales, binomial trees. The cleaner entry point before Volume II.

Source: Shreve ↗

• Chapters 1-5 in order
• Every exercise in chapters 1 and 2 (binomial model, risk-neutral measure)
• Derive the Black-Scholes formula from the binomial limit before moving to Vol II

Quant Interview - Recruiting Season · due 2027-10-31 · 20h · critical

Quant trading firms (Jane Street, Citadel, Two Sigma, Optiver, DRW, IMC, SIG) recruit juniors in September-November for the following summer. This is the primary internship recruiting window. By this point Green Book, Heard, and Shreve I are done — the math foundation is real. The job now is converting that into interview performance: resume, mock technical screens, probability problem sprints, and targeted outreach.

Source: Firm careers pages, LinkedIn, Glassdoor ↗

• By August 31: resume finalized — lead with Putnam performance, math coursework, C++ and Python projects
• September: apply to all target firms; Jane Street and Citadel open early — apply the day applications open
• October: start mock probability + brainteaser sessions 3x per week using Green Book and Heard problems timed
• October-November: mock technical phone screen with a friend or via interviewing.io; target sub-5-minute Green Book problems cold

Quant Interview - Products · due 2027-12-01 · 35h · high

The practitioner's options book. Hull teaches you how to derive the Black-Scholes formula; Natenberg teaches you how traders actually think about options. Volatility as a tradeable asset, skew, term structure, risk management for an options book, the psychology of pricing. Jane Street, Citadel, and Optiver traders read this before they read Hull. The two books are complementary: Natenberg is the intuition layer, Hull is the mathematical derivation layer. Read Natenberg first — it makes Hull's formulas land with practical meaning.

Source: Sheldon Natenberg ↗

• Chapters 1-8: option fundamentals, theoretical value, delta — build the intuition before any formula
• Chapters 9-14: risk measurement, the Greeks in practice, volatility spreads — this is the trading interview layer
• Chapter 19 (volatility skew) and Chapter 20 (risk management) — how real desks think about books
• After each chapter: look at actual options chains and find the concept in live data — skew, term structure, put/call parity violations

Quant Interview - Products · due 2028-01-01 · 60h · high

Options, futures, swaps, hedging strategies, Greeks, volatility surfaces, exotic products. The product knowledge layer every quant needs. Read after Shreve I - Hull connects the stochastic math to live market instruments.

Source: Hull ↗

• Chapters 1-20 core
• Chapter 19 (Greek letters) must be known cold - every interview assumes this
• Run live options chains alongside each chapter to connect theory to real prices

Quant Interview - Game Theory · due 2028-07-01 · 50h · medium

Nash equilibria, dominant strategies, Bayesian games, auctions, mechanism design. Jane Street and other trading firms care deeply about game theory - auctions, strategic interaction, and equilibrium reasoning appear constantly in trading decisions and interviews.

Source: Osborne ↗

• Chapters 1-9 core (strategic games through Bayesian games)
• Chapter 9 (auctions) is directly interview-relevant - read it twice
• Every equilibrium: write the strategy profile and verify no player wants to deviate

Quant Interview - Econometrics · due 2028-07-01 · 60h · medium

Regression with time-series data, instrumental variables, panel data, difference-in-differences, and causal inference. Quant researchers use these constantly - the gap between mathematical statistics and applied empirical work. The accessible applied treatment before Greene.

Source: Stock & Watson ↗

• Chapters 1-14 core (regression through time series)
• Chapter 12 (instrumental variables) - one of the most important causal inference tools
• Run every example in Python/R alongside reading to build hands-on fluency

Quant Interview - ML Theory · due 2028-08-01 · 80h · medium

Free online. Linear methods, regularization, kernel methods, SVMs, neural networks, boosting, random forests - with full mathematical derivations. Modern quant research uses ML extensively. This is the mathematically rigorous treatment the field uses.

Source: Hastie, Tibshirani & Friedman ↗

• Chapters 1-12 core (regression through neural nets)
• Chapter 7 (model assessment and selection) is critical for anyone running backtests
• Pair with a Python ML project for each major method - theory without implementation is hollow

Quant Interview - Market Microstructure · due 2028-08-01 · 55h · medium

Order book dynamics, bid-ask spreads, adverse selection, price impact, market maker economics, trading mechanisms. The accessible standard for how markets actually work mechanically. Almost completely absent from purely mathematical training.

Source: Harris ↗

• Parts I-III (why people trade, order types, market structures)
• Chapter 14 (spread decomposition) is the most quantitatively important chapter
• Connect every concept to live Level II order book data - watch a liquid market while reading

Quant Interview - Market Microstructure · due 2028-09-01 · 70h · medium

The mathematical treatment of market microstructure: stochastic control for optimal execution, Almgren-Chriss model, market making with adverse selection, HFT strategies. The rigorous bridge from stochastic calculus (Shreve) to actual trading algorithms.

Source: Cartea, Jaimungal & Penalva ↗

• Chapters 1-7 core (from price impact to market making)
• Read after Shreve II - the stochastic control machinery comes directly from there
• Chapter 4 (optimal execution) is the most widely cited chapter in the HFT literature

Quant Interview - Core · due 2028-10-01 · 30h · high

Stochastic calculus and derivatives questions at the level Jane Street and Citadel actually ask. Harder than the Green Book.

Source: Joshi & Dowson ↗

• Chapters 1-8 (interview questions and intuitions)
• Do not open until Shreve II is at least 50% complete
• For each question you can't solve: trace the gap back to a specific math book

Quant Problems - Final Season · starts 2028-10-01 · due 2028-12-15 · 25h · high

Application-season quant work as pure problem practice from named sources.

Source: Zhou, Joshi, Brainstellar ↗

• Solve 30 hard Green Book probability/statistics/finance problems
• Solve 20 Joshi stochastic calculus or derivatives questions
• Solve 25 Brainstellar probability and logic puzzles cold

Quant Problems - Graduation · starts 2029-04-01 · due 2029-06-15 · 30h · high

Final-quarter quant problem bank. Count only solved probability, stochastic calculus, finance, and logic problems from named sources.

Source: Mosteller / Green Book / Joshi / Brainstellar ↗

• Redo all missed Mosteller problems
• Solve 20 fresh Green Book or Heard on the Street problems
• Solve 15 Joshi or Brainstellar hard problems with full written reasoning

Phase 1 - Summer 2026 · due 2026-08-01 · 60h · critical

The most comprehensive free C++ tutorial available. Complete it before opening Stroustrup - it fills every gap between knowing programming and knowing C++. Covers modern C++17/20 idioms, memory model basics, and common pitfalls.

Source: learncpp.com ↗

• Chapters 1-20 in order - every chapter, no skipping
• Write every code example in your editor and verify it compiles
• Before Stroustrup: learncpp chapters 1-10. After Stroustrup: chapters 11-20

Phase 1 - Gap Filling Only · due 2026-09-01 · 20h · low

Use only for targeted gap filling - when a specific computational skill (integration technique, matrix operation, basic probability) is blocking progress on a book. Khan Academy explains the mechanics; the books give the understanding. Never use as a primary resource.

Source: khanacademy.org ↗

• Calculus integration techniques: use only when Rudin assumes a computation you can't do
• Linear algebra operations: use only when Axler's notation is blocking a computation
• Probability basics: use only before Blitzstein if expected value intuition is missing
• 10-minute sessions maximum - look up the specific skill and return to the book

Phase 1 - Summer 2026 · due 2026-10-01 · 30h · medium

Free C++ exercises with optional human mentorship. The C++ track covers modern idioms - templates, RAII, move semantics, the STL - through small focused exercises. Use alongside learncpp.com in Phase 1 to get hands-on practice and human feedback on your C++ style before the project phase begins.

Source: exercism.org ↗

• Complete the core C++ track (first 20 exercises minimum)
• Request mentor feedback on at least 5 exercises - the feedback is valuable and free
• Focus on exercises involving iterators, templates, and smart pointers
• Done when: every exercise on the core track passes your own code review standard

Phase 1 - Intuition Building · due 2027-01-01 · 25h · medium

Grant Sanderson's visual mathematics series. Not a replacement for books - a geometric intuition builder before and alongside them. The linear algebra, calculus, and neural network series each provide spatial understanding that Axler, Rudin, and ESL assume but never explicitly build.

Source: youtube.com/@3blue1brown ↗

• Essence of Linear Algebra (16 videos): watch before starting Axler chapter 1
• Essence of Calculus (12 videos): watch before starting Rudin
• Neural networks series: watch before or alongside ESL chapters 11-12
• After each series: identify what visual intuition you now have that would have helped earlier

Phase 1 - Foundation · due 2027-01-01 · 40h · low

Interactive courses with immediate feedback. Best used in Phase 1 to build intuition before the heavy book-based self-study begins. The combinatorics, number theory, and probability courses are well-designed. Not a substitute for books - a warmup tool.

Source: brilliant.org ↗

• Number Theory course: complete before AoPS Introduction to Number Theory
• Combinatorics course: complete before AoPS Counting and Probability
• Computer Science Fundamentals: complements the CS lane in Phase 1
• Stop using Brilliant once the primary book-based lanes are fully active

Phase 2 - Ongoing · due 2027-06-01 · 40h · medium

Evan Chen's free handouts, blog posts, and LaTeX templates for competition mathematics. His proof-writing style guide is essential before submitting any written competition solution. His handouts cover specific Putnam technique families with carefully chosen problems.

Source: evanchen.cc ↗

• OTIS excerpts: use the publicly available handouts for technique drilling
• Proof-writing guide: read before writing up any Putnam solution
• Blog posts on specific problems: use for alternate solution study
• napkin.pdf - his informal notes covering graduate math at accessible depth

Phase 1 - Ongoing Reference · due 2027-06-01 · 40h · medium

Free exhaustive notes on calculus, linear algebra, and differential equations. Use as a rapid-access reference when Rudin or Arnold is too terse on a specific computation. Not a substitute for the books - a lookup tool.

Source: Paul Dawkins - tutorial.math.lamar.edu ↗

• Calculus I-III sections: use when computing specific derivatives or integrals
• Differential Equations section: use alongside Arnold and Tenenbaum for technique checks
• Linear Algebra section: use when Axler's abstract approach needs a computational anchor

Phase 1 - Summer 2026 · due 2027-06-01 · 50h · high

Math-programming problems that force you to combine number theory, combinatorics, and efficient C++ simultaneously. The bridge between pure math self-study and applied computation. Problems 1-50 are accessible early; 51-100 require real mathematical depth.

Source: projecteuler.net ↗

• Problems 1-25 in Summer 2026 alongside C++ foundation
• Problems 26-60 through Autumn 2026 alongside Rudin and Dummit
• Problems 61-100 through Spring 2027 - require number theory and combinatorics
• Write every solution in C++ - never use Python here

Phase 2 - Autumn 2026 · due 2027-09-01 · 60h · high

The essential first LeetCode milestone. NeetCode organizes 150 problems by pattern - arrays, two-pointer, sliding window, binary search, trees, graphs, DP, backtracking. After completing this you know every major algorithmic pattern. You will not be fast yet. Speed comes from the next milestone.

Source: neetcode.io ↗

• Complete each topic block fully before moving to the next - order matters
• 25 minutes solo per problem, then watch the explanation if stuck
• Re-solve every miss within 5 days - pattern recognition, not memorization
• Milestone check: after NeetCode 150, you should be able to identify the correct pattern for any medium within 2-3 minutes. If not, re-do the weak topic blocks before moving on

Phase 2 - Autumn 2026 · due 2027-09-01 · 45h · medium

Free structured competitive programming curriculum from Bronze to Platinum. The Gold level problems require mathematical depth - graph theory, DP on trees, number theory - that overlaps directly with Putnam combinatorics. Use as a structured algorithm curriculum before Codeforces free practice.

Source: usaco.guide ↗

• Bronze complete by end of Summer 2026
• Silver complete by Winter 2027
• Gold begin Spring 2027 - the mathematical difficulty is significant
• Each module: read the concept, solve the recommended problems, move on

Phase 2 - Sophomore Summer through Junior Year · due 2027-12-01 · 60h · high

The MIT Putnam seminar materials, freely available. Zhao's handouts are the highest-quality free training materials for Putnam-level problem solving. Each handout is a masterclass on a specific technique or topic area.

Source: yufeizhao.com/olympiad ↗

• Algebra: quadratic residues, polynomials, functional equations handouts
• Combinatorics: probabilistic method, graph theory, extremal combinatorics
• Number theory: valuations, Zsygmondy, multiplicative functions
• Work one handout per month during junior year, increasing to one per two weeks in senior year

Phase 3 - Winter 2027-2028 · due 2028-02-28 · 75h · high

The 'good at LeetCode' threshold for quant firms is ~300 mediums total (NeetCode 150 + 150 more), solved consistently under 20 minutes on problems you have not seen. Count matters less than speed - 200 problems at sub-20 pace beats 400 where you needed hints. This milestone is your technical interview green light.

Source: leetcode.com ↗

• Target: any unseen medium solved and submitted in under 20 minutes
• Drill by company tag: 'Jane Street', 'Goldman Sachs', 'Citadel', 'Two Sigma'
• Track your average solve time weekly - if not improving, identify the slow pattern
• You are 'good' when: 10 random mediums in a row, all under 20 min, all correct on first submission

Competition - Summer 2027-2028 · due 2028-08-01 · 20h · low

Annual international undergraduate mathematics competition held in July/August in Bulgaria. Problems sit at Putnam difficulty or harder, with strong emphasis on analysis and linear algebra. Provides external international ranking and is recognized by European PhD programs. Application is free; travel is the cost.

Source: imc-math.org.uk ↗

• Apply for 2027 or 2028 - depends on REU schedule
• Problems 1-3 are Putnam A2/B2 difficulty - target full solutions there
• Problems 4-5 are graduate qualifier level - attempt with no expectation
• Results go directly on the PhD application - list alongside Putnam

Phase 4 - ML Implementation · due 2028-08-01 · 45h · high

The practical ML implementation layer that pairs with ESL. PyTorch is not a replacement for probability/statistics or ESL theory; it is how you turn models into working notebooks, debug gradients, and build credible quant/research artifacts.

Source: pytorch.org tutorials + personal notebooks ↗

• Start only after Python, NumPy, Pandas, and basic linear algebra are usable
• Tensors, autograd, datasets, training loops, evaluation, and reproducibility
• Build two small projects: one supervised model and one time-series or market-data model

Phase 2 - Junior Year · due 2028-09-01 · 80h · high

Competitive programming at scale. Codeforces rating 1200-1600 builds algorithmic speed; 1600-2000 requires deep insight. The mathematical difficulty at 1800-2000 rated overlaps with Putnam A3/B3 difficulty.

Source: codeforces.com ↗

• Begin 1200-rated problems Autumn 2026 alongside LeetCode
• Reach 1600 rated consistently by Summer 2027
• Work 1600-2000 problems in junior year alongside the NeetCode roadmap
• Use Codeforces EDU section for structured topic-by-topic drilling

Phase 4 - Summer 2028 · due 2028-09-01 · 50h · high

Elite quant firm technical screens include hard problems. 50 targeted hards brings you to sub-45-minute pace on any hard problem type. This is not about count - it is about eliminating the gap between medium competence and hard competence. Complete all 50 before September 2028. November is Putnam sprint - no new problems after that.

Source: leetcode.com ↗

• Start only after 300 mediums are at consistent sub-20-minute pace
• Prioritize: DP hard (most common in quant screens), graph hard, interval hard
• For each miss: identify the exact insight gap - almost always one small observation
• You are done when: any hard problem attempted with no prior exposure, solved within 45 minutes

Quant Practice - Junior Year · due 2028-10-01 · 30h · high

Free collection of probability and logic puzzles used verbatim in quant interviews at Jane Street, Citadel, and Two Sigma. Many Heard on the Street and Green Book problems appear here with worked solutions. Use after completing Mosteller - the difficulty level is Mosteller Brainstellar live interview.

Source: brainstellar.com ↗

• Hard probability section: do not look at solutions for at least 20 minutes
• Dynamic programming puzzles: these overlap with the harder LeetCode medium patterns
• Geometric probability problems: gap for most candidates - drill these specifically
• After each session: write up your best approach in one clean paragraph

Quant Practice - Junior Year · due 2028-10-01 · 20h · medium

Paid platform for AI-driven quant interview simulations used by candidates targeting Jane Street, Citadel, and Two Sigma. Covers probability, brain teasers, and market intuition under time pressure. Worth 1-2 months before recruiting season - not a year-round subscription. Green Book and Brainstellar cover the same content for free; GetCracked adds the conversational timed pressure that mirrors a real phone screen.

Source: getcracked.io (paid) ↗

• Subscribe for 1-2 months before first junior-year quant screens
• Probability and brain teaser modules only after Mosteller and Green Book are stable
• Track which question types fail under time pressure versus solo practice
• Cancel after recruiting season - value is in the practice pressure not the content

Quant Practice - Junior Year · due 2028-10-01 · 40h · high

Curated quant interview questions across probability, statistics, combinatorics, brain teasers, and market intuition - the actual question types Jane Street, Citadel, and Optiver use in screens. More targeted than LeetCode for the mathematical probability section of quant interviews.

Source: quantquestions.io ↗

• Complete all probability sections before any firm screen
• Brain teaser section: solve each without hints, time yourself strictly
• Market intuition section: complements Harris and Hull reading
• Wrong answers: trace each gap back to a specific book (Blitzstein, Mosteller, or Joshi)

Quant Practice - Senior Year · due 2028-11-01 · 15h · medium

Real interview questions reported by candidates at Jane Street, Citadel, IMC, Optiver, and Two Sigma. Not a practice platform - an intelligence source. Read the interview reports for your target firms 2-3 months before recruiting season to understand what each firm actually emphasizes.

Source: glassdoor.com ↗

• Jane Street: known for probability, game theory, and market making puzzles
• Citadel: heavier on statistics, econometrics, and ML theory than JS
• IMC: strong emphasis on C++ systems and options pricing
• Read at least 20 reports per firm before your first screen - patterns emerge quickly

Quant Practice - Stretch Signal · due 2028-11-01 · 15h · medium

Jane Street puzzles are genuinely hard stretch problems, not a daily baseline like LeetCode. Use them as occasional deep-work signals once probability, combinatorics, and proof writeups are already improving. A serious attempt plus a clean gap note counts; do not let this crowd out core LeetCode, Green Book, or Putnam work.

Source: janestreet.com/puzzles ↗

• Start with older archive puzzles only after the 2026 Putnam attempt
• One serious attempt can count even if you need solution study afterward
• Submit only when the solution is genuinely clean
• Harder current-month puzzles are optional stretch, not a recurring burden

Competition - Annual · due 2028-11-01 · 20h · medium

Free annual competition held each autumn, open to all undergraduates. 2.5 hours, 7 problems. Difficulty sits between Putnam A2/B2 and A4/B4 - an ideal calibration tool before each December Putnam. Cheaper than a full Putnam mock because you get external ranking and official results.

Source: vtregionalmath.math.vt.edu ↗

• Enter every year from Autumn 2026 through Autumn 2028
• Use as a mid-semester calibration: where are you relative to target
• The VTRMC problems recycle from similar families as Putnam - treat it as a real exam
• After results: cross-reference your score against your current Putnam mastery self-ratings

Daily - All Phases · due 2028-12-01 · 20h · medium

Spaced repetition for definitions, theorem statements, and algorithm templates. This is maintenance, not a second curriculum. Keep the deck small and high-signal: only cards that remove real recall friction. A 10-minute cap matters more than a huge card count.

Source: apps.ankiweb.net ↗

• Start with 20 high-value cards, not 100
• Add cards only from books you are actively using
• Delete or suspend cards that feel like trivia
• Daily review session: 10 minutes maximum - log if over and cut the deck

Phase 1 - Ongoing · due 2028-12-01 · 80h · high

The central online competition math community. Use the forum to check your solutions, find alternate approaches, and read how strong solvers think. Use the wiki for instant lookup of any competition technique. Use the problem archives for additional Putnam drilling.

Source: artofproblemsolving.com ↗

• After every hard Putnam problem: search AoPS for the thread, compare approaches
• Contribute solution write-ups - writing forces clarity and gets feedback
• Use the Putnam archive to drill specific years and problem slots (A1-A6, B1-B6)

Phase 1 - Ongoing · due 2028-12-01 · 30h · medium

The best free mathematical Q&A platform. Use it in two directions: look up answers when stuck on a specific problem or theorem, and post your own solution write-ups to get feedback from stronger mathematicians. High-quality MSE answers on hard analysis and algebra questions often exceed textbook explanations.

Source: math.stackexchange.com ↗

• When stuck on Rudin for more than 30 minutes: search MSE before reading the solution
• Post your own proofs for feedback - the community identifies gaps you miss
• Putnam problems: every Putnam problem from the last 20 years has an MSE thread
• Build a searchable public record - your MSE profile with quality answers is visible to PhD programs

Daily - Always Active · due 2028-12-01 · 120h · critical

Daily 5-minute arithmetic sprints. Starts now and never stops. The single habit that compounds the most silently - arithmetic speed reduces cognitive overhead on every Putnam problem and every quant interview.

Source: zetamac.com ↗

• Score 80 by Autumn 2026
• Score 100 by Winter 2027
• Score 120 by Summer 2027
• Score 150 by junior year and maintain

CS/C++ - Summer 2026 URAP (Mitsch) · due 2026-06-11 · 20h · critical

Read BEFORE the first URAP meeting. Differential dynamic logic tutorial plus the robot collision-avoidance paper your quadcopter/flapper formalization extends. Install KeYmaera X and set up an Overleaf research journal.

Source: Mitsch / Platzer ↗

• Work through the KeYmaera X tutorial examples after installing
• Read morerobix collision-avoidance paper alongside the tutorial
• Open robix.kyx as the template your formalization follows
• Set up the Overleaf journal in technical-report structure

• Install KeYmaera X + set up Overleaf research journal2026-06-02
• Work through all KeYmaera X tutorial examples2026-06-06
• Read morerobix collision-avoidance paper + open robix.kyx template2026-06-10

backups: Differential dynamic logic tutorial (PDF) — The tool you use all summer - read before first meeting. · Robot collision avoidance paper (PDF) — Your project extends this work. · robix.kyx reference models (GitHub) — Template for the quadcopter formalization.

CS/C++ - Forge MaUWB ramp · starts 2026-06-06 · due 2026-06-15 · 24h · critical

This is the June 15 readiness sprint for the Forge/UWB project. The target is not generic C++; the target is knowing how to set up MaUWB boards, flash Anchor/Tag roles, read distance/RSSI, collect a 3+ anchor table, and attempt the first 2D trilateration/multilateration solve before June 15.

Source: Makerfabs MaUWB ESP32S3 docs / UWB-MaUWB-AT / Forge UWB repo ↗

• June 6-9: install Arduino/ESP32S3 toolchain, read Makerfabs MaUWB ESP32S3 usage, and identify the exact Tag0/Anchor0 examples plus UWB-MaUWB-AT examples
• June 10-11: configure Anchor0 and Tag0, record distance/RSSI over serial, and save a small CSV log; this proves ranging works
• June 12-13: understand the AT/library report format and make a parser/logger for time, anchor_id, tag_id, distance, RSSI
• June 14: configure 3+ anchors with fixed coordinates and collect one moving tag's distances to each anchor
• June 15: attempt the first 2D trilateration/multilateration solve and bring a readiness packet: board settings, logs, CSV, anchor coordinates, estimated vs known position, and failure notes

backups: Makerfabs MaUWB ESP32S3 UWB module wiki — Anchor/Tag setup, AT commands, multi-anchor/multi-tag distance and RSSI workflow. · Makerfabs MaUWB firmware/manual/demo repository — Firmware/manual/demo files for AT-command MaUWB modules. · UWB-MaUWB-AT Arduino library — Simplified Arduino interface for MaUWB tag/anchor modes and positioning applications. · Makerfabs indoor positioning test — Reference workflow for anchors, tag distance collection, UDP export, and coordinate calculation.

CS/C++ - Summer 2026 URAP (Mitsch) · due 2026-06-28 · 35h · critical

ODE foundation = the existing m1-diffeq item (MIT 18.03 Mattuck, Layer 1, due 2026-07-31): do that first for linear systems, phase planes, and eigenvalue stability. THIS item is the extra layer the URAP needs that 18.03 does not fully cover - nonlinear dynamics and Lyapunov functions - the exact tools for the URAP's stability + attractivity properties. Sync with Platzer ch 4-6 and finish before the quadcopter formalization (URAP weeks 5-7).

Source: Strogatz / Khalil ↗

• Fast June ramp: use 3Blue1Brown DE series for quick intuition; m1-diffeq (MIT 18.03) is the parallel deeper course you keep going in July
• Strogatz Ch 5-6: 2D linear systems, phase plane, classification of fixed points (problems 5.1.9, 5.2.1, 6.1.5, 6.3.1)
• Strogatz Ch 6.4-6.5 + 7: nullclines, conservative systems, limit cycles (problems 6.4.1, 7.2.5)
• Strogatz 7.2 / Khalil Ch 4: Lyapunov functions = the URAP's 'converge then stay close' (stability + attractivity)
• Map each result to Platzer: continuous dynamics -> ODEs -> dL differential invariants/cuts (ch 4-6)

• Strogatz Ch 5-6 phase plane + fixed points (problems 5.1.9, 5.2.1, 6.1.5, 6.3.1)2026-06-15
• Strogatz 6.4-6.5 + Ch 7 Lyapunov / limit cycles (problems 6.4.1, 7.2.5)2026-06-22
• Map nonlinear stability to Platzer dL differential invariants (ch 4-6)2026-06-28

backups: Strogatz - Nonlinear Dynamics and Chaos — Phase plane, fixed points, Lyapunov - the URAP stability/attractivity math. · Strogatz lecture videos (Cornell, free) — Author-taught companion to each book chapter. · MIT 18.03 ODEs - foundation (see m1-diffeq item for full dated schedule) — Do this first; the m1-diffeq tracker item has the lecture+problem-set schedule.

CS/C++ - Summer 2026 URAP (Mitsch) · due 2026-06-30 · 80h · critical

The URAP textbook. Differential dynamic logic, hybrid systems, safety and stability proofs. Watch the matching lecture video for EACH chapter - do not read a chapter without its lecture.

Source: Platzer ↗

• Ch 1-3 before June 11 (logic, modeling, dL basics)
• Ch 4-6 June weeks 1-2 (proofs, safety properties, hybrid systems)
• Ch 7-10 June weeks 3-4 (advanced modeling, stability)
• Reference all summer; run the KeYmaera X prover daily during the formalization weeks

• Ch 1-3 logic, modeling, dL basics (+ matching lfcps.org lectures)2026-06-09
• Ch 4-6 proofs, safety properties, hybrid systems (ODEs in dL)2026-06-18
• Ch 7-10 advanced modeling, stability2026-06-28

backups: Platzer LFCPS book (Springer) — Free via the Springer link Mitsch provided. · LFCPS slides + lecture videos — Watch the lecture matching each chapter BEFORE reading it.

CS/C++ - Foundation · due 2026-07-15 · 12h · critical

Basic developer fluency: navigate the filesystem, inspect files, use pipes, search with rg/grep, edit safely, run builds/tests, manage environment variables, and understand what a shell command is doing. This comes before serious C++, Git, CS:APP labs, or research code.

Source: MIT Missing Semester / Shell docs ↗

• Daily shell reps for real tasks, not passive videos
• Use pwd, cd, ls, mkdir, cp, mv, rm carefully, cat, less, head, tail, rg/grep, find, sort, uniq, wc, curl, ssh basics
• Goal: you can open a repo, find files, run tests, inspect logs, and explain every command you typed

CS/C++ - Fall 2026 DePaul prep · due 2026-08-01 · 50h · high

CSC300/301 assume Java and examine you ON PAPER (write Java by hand). Highest-leverage prep is Java syntax cold, not pre-reading the whole textbook. Get fluent enough to write data-structure code on paper in about 5 minutes.

Source: Horstmann / MOOC.fi ↗

• MOOC.fi Java Programming Parts 1-5 (interactive, immediate feedback)
• Horstmann 'Core Java for the Impatient' as reference (the CSC300 text)
• Practice writing Java BY HAND on paper - that is exactly how 300/301 exams work
• Then LeetCode easy then medium in JAVA (not Python) to drill algorithms + syntax together

• MOOC.fi Java Parts 1-3 (variables, loops, methods, objects)2026-07-08
• MOOC.fi Parts 4-5 + Horstmann ch 1-5 (collections, generics)2026-07-20
• 30 LeetCode easy in Java + rewrite 10 of them by hand on paper2026-08-01

backups: MOOC.fi Java Programming (U. Helsinki, free) — Best free Java course; interactive exercises. · Sedgewick & Wayne, Algorithms 4e (CSC300/301 text) — The actual course text + author videos. Let the courses drill it; pre-read only 1.1-1.3 for Java basics.

CS/C++ - Fall 2026 DePaul prep · due 2026-08-22 · 60h · high

This is the ACTUAL CSC300/301 skill, not Java syntax: implement and analyze each data structure in Java, test it with JUnit, then be able to rewrite it BY HAND in ~5 min (that is how the exams work). Watch a lecture, then immediately implement the structure yourself - do not just watch.

Source: Fiset / CS61B / Sedgewick ↗

• CSC300 structures: linked lists, stacks, queues, deques, resizable arrays, priority queues/heaps, union-find (Sedgewick 1.3-2.5)
• CSC301 structures: symbol tables, BSTs, balanced (red-black) BSTs, hash tables, graphs (BFS/DFS, MST, shortest paths), tries (Sedgewick 3.1-5.2)
• After each William Fiset video, implement that structure from scratch immediately, then re-do it on paper
• Do the CS61B projects - closest free equivalent to CSC300 + CSC301 combined
• Then NeetCode/LeetCode problems in Java filtered to the structure you just built

• CSC300 set from scratch: linked list, stack, queue, heap, union-find (Sedgewick 1.3-2.5)2026-08-03
• CS61B projects: Deque + Gitlet (or proj2/proj3)2026-08-13
• CSC301 set: BST, red-black BST, hash table, graph (BFS/DFS/MST/SP), trie (Sedgewick 3.1-5.2)2026-08-22

backups: William Fiset - Data Structures (YouTube, Java from scratch) — Implement every structure yourself right after watching. · CS61B UC Berkeley (free lectures + labs + projects) — Closest free equivalent to CSC300 + CSC301; do the projects. · Abdul Bari - Algorithms (YouTube) — Best visual algorithm + complexity-analysis lectures. · NeetCode.io roadmap — Pattern roadmap matched to each structure; do in Java.

CS/C++ - Fall 2026 DePaul prep · due 2026-08-31 · 40h · high

CSC373 is C + x86 assembly + GDB with three labs (data, bomb, buffer). Targeted prep is C basics plus GDB comfort. The labs and assembly are what the course teaches - do not pre-read all of CS:APP over a URAP + Putnam summer.

Source: Malan / Beej ↗

• CS50 weeks 1-4 (cover C directly) - Malan is exceptional
• Beej's Guide to C as the free reference
• One GDB session before fall (Beej covers it)
• Light skim CS:APP ch 1-2 only; let the course do ch 3 + the three labs

• CS50 weeks 1-2 (C, arrays, functions) + problem sets2026-08-08
• CS50 weeks 3-4 (memory, pointers) + Beej C guide2026-08-20
• One GDB session (Beej) + skim CS:APP ch 1-22026-08-31

backups: CS50 (Harvard, free) — Best C intro; do weeks 1-4. · Beej's Guide to C Programming — Free C reference. · CS:APP companion (CSC373 text + labs) — Course text; the labs are done in the course.

CS/C++ - Foundation · due 2026-09-01 · 10h · critical

Version control is non-negotiable at any technical firm. Git is expected from day one of any internship or research position. Pro Git is free online and covers everything needed for real collaborative work. Complete before any technical interviews or applications.

Source: Chacon & Straub (free at git-scm.com/book) ↗

• Chapters 1-3 (basics, branching, remote workflows) — read and practice each command live
• Chapter 7 (advanced tools: stash, cherry-pick, bisect, blame, rebase -i)
• Goal: never lose work, never be confused by merge conflicts, know exactly what git status, diff, log, and reset do

CS/C++ - Foundation · due 2026-09-01 · 30h · critical

Fast overview of modern C++ from its creator. Read first to get the whole picture before deep-diving with Meyers.

Source: Stroustrup ↗

• Read end-to-end in 2 weeks
• Build one small project in each chapter's style
• This is orientation, not mastery - Meyers follows

CS/C++ - Gamified practice (make it fun) · due 2026-10-01 · 30h · medium

When LeetCode burns you out, switch here. Same Java + data-structure + algorithm reflexes, but with ranks, games, and bot battles instead of a problem list. Do them in Java so it doubles as CSC300/301 prep.

Source: Codewars / CodinGame / Robocode ↗

• Codewars: kata with a martial-arts belt/rank system - level up from 8 kyu, choose Java
• CodinGame: write code to win actual games and bot battles; supports Java
• Robocode: write a Java tank AI that battles others - pure Java, real OOP and logic
• VisuAlgo: watch every data structure and algorithm animate - makes BSTs/heaps/graphs click
• CodeCombat: an RPG where you code to play - the lightest, funnest break

• Codewars: reach 5 kyu in Java2026-08-15
• Robocode: build a Java tank that wins a melee round2026-09-15

backups: Codewars (kata + belt ranks, Java) — Gamified kata with rank progression. · CodinGame (code games + bot battles) — Solve by writing code to win games; Java supported. · Robocode (Java tank battles) — Write a Java robot AI - fun and real Java. · VisuAlgo (data structure + algorithm visualizer) — See every DS/algorithm animate. · CodeCombat (learn to code as an RPG) — Funnest break; code to play the game.

CS/C++ - Gamified practice (make it fun) · due 2026-10-15 · 25h · medium

CSC373's bomb lab and buffer lab are reverse-engineering + memory-safety puzzles. These sites are literally that, gamified: assembly, GDB, and buffer overflows as CTF challenges. The funnest way to walk into the 373 labs already comfortable.

Source: Microcorruption / pwn.college / OverTheWire ↗

• Microcorruption: embedded-security CTF - reverse-engineer assembly to unlock locks; basically the bomb lab as a game
• pwn.college: structured binary-exploitation course with levels - assembly, GDB, memory safety
• OverTheWire 'Bandit' then 'Narnia': Linux + C/exploitation wargames with a gentle ramp
• These drill x86 + GDB + buffer overflows - exactly CSC373 ch 3 plus the bomb and buffer labs

• OverTheWire Bandit levels 0-152026-08-20
• Microcorruption: first 5 locks (Tutorial -> New Orleans -> Sydney)2026-09-10
• pwn.college: assembly-crash-course + GDB + memory-errors modules2026-10-01

backups: Microcorruption (embedded CTF - assembly + GDB feel) — Bomb-lab-as-a-game; reverse-engineer to win. · pwn.college (binary exploitation, leveled) — Structured assembly + memory-safety course with levels. · OverTheWire wargames (Bandit -> Narnia) — Linux + C/exploitation wargames; gentle ramp.

CS/C++ - Foundation · due 2026-12-01 · 55h · critical

The real C++ education. Move semantics, rvalue references, smart pointers, perfect forwarding, lambda captures, concurrency basics.

Source: Meyers ↗

• All 42 items in order
• For each item: read, implement the bad version, implement the good version, compare
• Items 23-30 (move semantics) are the highest priority - read twice

CS/C++ - LeetCode aligned to CodePath TIP102/103 · due 2026-12-15 · 80h · medium

Cover every CodePath TIP102/103 unit with LeetCode in Java. Four tiers per topic: (1) TIP102 HackerRank assessment, (2) TIP103 HackerRank assessment, (3) NeetCode pattern video + problems, (4) LeetCode filtered to that topic, easy then medium. The same 12 topics power CSC300/301, so do every tier in Java.

Source: CodePath / NeetCode / LeetCode ↗

• Unit 1 Strings & arrays -> LeetCode tags Array, String, Two Pointers, Sliding Window
• Unit 2 Dictionaries/hashmaps -> Hash Table, frequency maps (NeetCode 'Arrays & Hashing')
• Unit 3 Stacks, queues, two pointer -> Stack, Queue, Monotonic Stack, Two Pointers
• Unit 4 Review + Big O -> mixed set from units 1-3; re-derive time/space for each
• Unit 5 Linked lists I + OOP -> Linked List traversal/insert/delete, slow-fast pointer
• Unit 6 Linked lists II + Recursion I -> Linked List reversal/cycle, basic recursion
• Unit 7 Recursion II + Binary search -> Binary Search, Divide & Conquer, recursion trees
• Unit 8 Binary trees I -> Tree traversal (in/pre/post, BFS) (NeetCode 'Trees')
• Unit 9 Binary trees II -> BST, tree DFS/BFS, root-to-leaf path problems
• Unit 10 Graphs -> Graph BFS/DFS, Topological Sort, Dijkstra, Union-Find (NeetCode 'Graphs')
• Unit 11 Matrices -> Matrix / grid BFS/DFS, in-place operations
• Unit 12 Dynamic Programming -> memoization, tabulation, backtracking, greedy (NeetCode '1-D & 2-D DP')

• CodePath Units 1-4: arrays/strings, hashmaps, stacks/queues, Big-O review2026-10-01
• Units 5-7: linked lists I+II, recursion, binary search2026-10-25
• Units 8-9: binary trees I + II2026-11-15
• Units 10-12: graphs, matrices, dynamic programming2026-12-15

backups: NeetCode 150 / Practice (pattern per topic) — Watch the pattern, then do the problems - matches the CodePath units. · LeetCode problem set (filter by topic tag, do in Java) — Easy then medium, filtered to the current CodePath unit's tag. · CodePath (TIP102 + TIP103 portal) — Your enrolled courses; TIP102 gentler pass, TIP103 harder pass, same 12 units.

CS/C++ - Algorithms · due 2027-03-15 · 30h · high

Post-Putnam winter implementation block. This is real coding reps, not platform browsing: implement patterns in C++, re-solve misses, and build speed before the heavier recruiting push.

Source: NeetCode / USACO / C++ implementations ↗

• Complete 40 NeetCode easy/medium problems in C++ with clean re-solves
• Finish USACO Silver prerequisites that overlap with graphs, prefix sums, binary search, and DP
• Every miss gets a short repair note and a second solve within 7 days

CS/C++ - Python for Quant · due 2027-04-01 · 40h · critical

Python is the language of quant research. Every trading firm uses Python for data analysis, backtesting, research notebooks, and tooling — even the C++ shops. The plan teaches C++ deeply but touches Python only as a footnote in ESL and econometrics. This must be fixed before Fall 2027 recruiting. Core resources: Python official docs (python.org), NumPy quickstart, Pandas user guide, Automate the Boring Stuff (free, automatetheboringstuff.com). All free.

Source: Python docs, NumPy, Pandas, automatetheboringstuff.com ↗

• Week 1-2: Python core — loops, functions, classes, list comprehensions, file I/O, decorators
• Week 3-4: NumPy — ndarray operations, vectorized math, broadcasting, linear algebra module
• Week 5-6: Pandas — DataFrames, groupby, merge, time-series indexing with DatetimeIndex
• Capstone: pull historical price data via yfinance and backtest a simple momentum strategy end-to-end

CS/C++ - Competitive Programming · due 2027-06-01 · 50h · medium

Algorithms and data structures for competitive programming. Complements CLRS with implementation focus.

Source: Halim ↗

• Work alongside LeetCode hard and Codeforces 1600-2000
• Each topic chapter: read, code the template, solve 5 problems using it
• LeetCode hard and Codeforces 1600-2000 rated are parallel practice tools

CS/C++ - Systems · due 2027-06-01 · 80h · high

How programs run: bits, assembly, memory hierarchy, caching, linking, control flow, virtual memory, concurrency.

Source: Bryant & O'Hallaron (CS:APP) ↗

• Chapters 1-12 in order
• Complete every lab (datalab, bomblab, attacklab, cachelab, shelllab, proxylab)
• Cache and memory hierarchy chapters are the highest ROI for quant systems work

CS/C++ - Python for Quant · due 2027-07-01 · 35h · high

Build a real backtesting engine in Python that you can show in interviews. Not a tutorial — an original system you designed. This is how you demonstrate Python fluency beyond 'I read the docs.' A backtester forces you to handle real data problems: missing prices, corporate actions, lookahead bias, slippage modeling, and performance metrics (Sharpe, max drawdown, hit rate). When a recruiter asks 'have you built anything in Python?' this is the answer.

Source: Personal project — Python, Pandas, yfinance ↗

• Core engine: portfolio object that tracks positions, cash, and P&L tick by tick over historical data
• Signal layer: implement at least 3 distinct strategies — momentum, mean reversion, and a simple pairs trade
• Risk controls: max position size, stop loss logic, volatility scaling
• Output: equity curve plot, Sharpe ratio, max drawdown, and win rate per strategy — presented clearly in a Jupyter notebook
• Host on GitHub with a clean README — this is a portfolio item, treat it like one

CS/C++ - Algorithms · due 2027-08-01 · 40h · high

Chapters 1-8 of the authoritative algorithms reference. This is the foundations and sorting core: mathematical tools for analysis, asymptotic notation, divide-and-conquer with the master theorem, probabilistic analysis, heapsort, quicksort, and linear-time sorting. CLRS does not just present algorithms — it proves them. Loop invariants, recurrence trees, and exchange arguments are the reasoning patterns that distinguish top-firm SWE and quant dev candidates from LeetCode grinders. Halim (Competitive Programming 3) teaches you to code fast; these 8 chapters teach you to prove your code is correct and understand its true complexity.

Source: Cormen, Leiserson, Rivest, Stein (CLRS) ↗

• Ch. 1-3: roles of algorithms, asymptotic notation (Theta, O, Omega) — derive every bound, do not just recognize it
• Ch. 4: divide-and-conquer master theorem — derive all three cases; apply to merge sort, matrix multiplication
• Ch. 5: probabilistic analysis and randomized algorithms — this is the probability chapter, connects to quant interview style
• Ch. 6-7: heapsort and quicksort — write the correctness proof for each, not just the code
• Ch. 8: counting sort, radix sort, bucket sort — understand when and why comparison-based lower bound breaks

CS/C++ - Foundation · due 2027-09-01 · 30h · high

Jane Street's primary language is OCaml — they are the largest industrial OCaml shop in the world. Every line of production code at Jane Street is OCaml. They say they will teach it, but arriving with OCaml fluency is a genuine edge: it signals you understand functional programming, type systems, and the design principles Jane Street cares about. Real World OCaml is free online, written by Jane Street engineers. The focus is practical OCaml: the Core library (Jane Street's standard library), pattern matching, functors, modules, async I/O. After Python and C++, functional programming will feel alien at first — lean into the type system, it's the point.

Source: Minsky, Madhavapeddy, Hickey (free at dev.realworldocaml.org) ↗

• Part I (language concepts): read chapters 1-7 — variables, functions, lists, patterns, modules, records, variants
• Part II (tools and techniques): chapter 8 (functors) is the hard conceptual chapter — Jane Street's code is heavily functor-based
• Build one small command-line tool in OCaml — a calculator, a simple parser, anything — to force yourself through the build system and module structure
• Read Jane Street's tech blog (blog.janestreet.com) alongside — the posts explain why OCaml's type system catches entire categories of trading bugs that C++ does not

CS/C++ - Systems · due 2027-09-01 · 55h · high

Virtualization (processes, threads, scheduling), concurrency (locks, semaphores, CVs), persistence (file systems, journaling).

Source: Arpaci-Dusseau (OSTEP) ↗

• All three sections in order (free at ostep.org)
• Do all homework problems
• Concurrency section demands extra time - this is where systems bugs live

CS/C++ - Performance · due 2027-12-01 · 30h · medium

Pipeline stages, instruction-level parallelism, superscalar execution, caches, branch prediction, SIMD — explained with diagrams before they appear as cryptic numbers in perf profiles. Read this before Bakhvalov. Bakhvalov tells you what the CPU does and how to measure it; Inside the Machine tells you why the hardware behaves that way. The combination turns profiler output from noise into signal. Essential hardware intuition layer for anyone writing latency-sensitive C++.

Source: Jon Stokes ↗

• Parts I-II: pipeline basics and superscalar execution — the foundation for everything in Bakhvalov
• Part III: SIMD and vector units — directly relevant to any numerical C++ work
• After each chapter: open a perf profile from one of your C++ projects and find the concept you just read about

CS/C++ - OS & Low Level · due 2027-12-01 · 40h · medium

Linux syscalls, file I/O, process management, signals, IPC, memory management. The layer below the OS textbook.

Source: Love ↗

• Chapters 1-9 core
• Implement every major syscall family from scratch
• Pairs with OSTEP - read the OSTEP concept then the Love implementation

CS/C++ - Concurrency · due 2028-01-01 · 50h · high

Threads, mutexes, condition variables, atomics, lock-free programming, the C++ memory model. Critical for quant systems.

Source: Williams ↗

• Chapters 1-8 core
• Chapter 5 (C++ memory model) is the hardest - read it three times
• Implement a lock-free queue and a thread pool from scratch