Course Preparation (Booklist)
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Reference
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CourseTopicCommon TextbooksOther reading materialOther media (mostly YouTube videos)
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1ACalculusStewart, Single Variable Calculus
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1B; H1BCalculusStewart, Single Variable Calculus
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10ACalculus; Statistics; Combinatorics
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10BCalculus; Statistics; Combinatorics
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16AAnalytic Geometry; CalculusGoldstein, Lay, Schneider & Asmar, Calculus & It’s Applications
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16BAnalytic Geometry; CalculusGoldstein, Lay, Schneider & Asmar, Calculus & It’s Applications
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24Film; FictionPolster & Ross, Math Goes to the Movies.
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32PrecalculusAxler, Precalculus: A Prelude to Calculus; Cohen, Lee & Sklar, Precalculus.
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53; H53Multivariable CalculusStewart, Multiple Variable Calculus.MIT 18.02
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54; H54Linear Algebra; Differential EquationsLay, Nagle, Saff & Snider, Linear Algebra & Differential Equations.MIT 18.06
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55Discrete MathematicsRosen, Discrete Mathematics and its Applications.
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104AnalysisRudin, Principles of Mathematical Analysis; Ross, Elementary Analysis: The Theory of Calculus; Pugh, Real Mathematical Analysis.Jiří Leb, Basic Analysis: Introduction to Real AnalysisHarvey Mudd 131
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105AnalysisRudin, Principles of Mathematical Analysis; Pugh, Real Mathematical Analysis.
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110; H110Linear AlgebraFriedberg, Insel & Spence, Linear Algebra; Axler, Linear Algebra Done Right.
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113; H113Abstract AlgebraDumit & Foote, Abstract Algebra; Fraleigh, A First Course in Abstract Algebra; Hungerford, Abstract Algebra: An Introduction.Goodman, Algebra: Abstract and Concrete
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114Abstract Algebra; Galois Theory; Field TheoryArtin, Algebra; Escofier, Galois Theory; Stewart, Galois Theory; MacLane & Birkoff, Algebra; Artin, Galois Theory: Lectures Delivered at the University of Notre dame by Emil Artin.
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115Number TheoryNiven, Zuckerman & Montgomery, An Introduction to the Theory of Numbers
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116CryptographyHoffstein, Pipher & Silverman, An Introduction to Mathematical Cryptography.
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118Fourier AnalysisBoggess & Narcowich, A First Course in Wavelets with Fourier Analysis.
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121AEngineering Tools; Physical SciencesBoas, Mathematical Methods in the Physical Sciences.
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123ODEArnold, Ordinary Differential Equations; Brauer & Nohel, The Qualitative Theory of Ordinary Differential Equations: An Introduction.
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125ALogicHinman, Fundamentals of Mathematical Logic; Rautenberg, A Concise Introduction to Mathematical Logic; Enderton, A Mathematical Introduction to Logic.
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126PDEStrauss, Partial Differential Equations: An Introduction; Salsa, Partial Differential Equations in Action.
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127Mathematical BiologyAllman & Rhodes, Mathematical Models in Biology.
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128A; 128BNumerical AnalysisBurden & Faires, Numerical Analysis; Sauer, Numerical Analysis; Isaacson & Keller, Analysis of Numerical Methods; Stoer & Bulirsch, An Introduction to Numerical Analysis.
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130Classical GeometryHartshorne, Geometry: Euclid and Beyond; Euclid, The Thirteen Books of the Elements.
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135Set TheoryEnderton, Elements of Set Theory.
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136Incompleteness; UndecidabilityCutland, Computability: An Introduction to Recursive Function Theory.
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140Metric Differential GeometryBanchoff & Lovett, Differential Geometry of Curves and Surfaces.
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141Differential TopologyGuillemin & Pollack, Differential Topology; Milnor, Topology from the Differentiable Viewpoint; Munkres, Analysis on Manifolds; Spivak, Calculus on Manifolds; Kinsey, Topology of Surfaces.Differential Topology - John Milnor
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142Algebraic TopologyMunkres, Elements of Algebraic Topology; Armstrong, Basic Topology; Munkres, Topology.
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143Algebraic GeometryHasset, Introduction to Algebraic Geometry; Cox, Little & O'Shea, Ideals, Varieties, and Algorithms:An Introduction to Computational Algebraic Geometry and Commutative Algebra.
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151Secondary School Curriculum
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152Secondary School Curriculum
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153Secondary School Curriculum
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160History of MathematicsEdwards, The Historical Development of the Calculus.
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170OptimizationPablo Pedregal, Introduction to Optimization; Franklin, Methods of Mathematical Economics:Linear and Nonlinear Programming Fixed-Point Theorems.
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172CombinatoricsLint & Wilson, A Course in Combinatorics.Bondy & Murty, Graph Theory; Diestel, Graph Theory; Harary, Graph Theory; Fulton, Young Tableaux.
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185; H185Complex AnalysisBrown & Churchill, Complex Variables and Applications; Stein & Shakarchi, Complex Analysis; Gamelin, Complex Analysis; Sarason, Notes on Complex Function Theory; Cartan, Elementary Theory of Analytic Functions of One or Several Complex Variables; Spiegel, Lipschutz, Schiller & Spellman, Schaum's Outline of Complex Variables; Needham, Visual Complex Analysis; Bak & Newman, Complex Analysis.
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189Classical Mechanics; Quantum MechanicsFaddeev & Yakubovskii, Lectures on Quantum Mechanics for Mathematics Students; Arnold, Mathematical Methods of Classical Mechanics; Hannabuss, An Introduction to Quantum Theory.
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191Putnam; Problem SolvingLozansky & Rousseau, Winning Solutions.Kedlaya, Poonen & Vakil, The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions and Commentary.
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191Knot TheoryAdams, The Knot Book.
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202A; 202BAnalysis; TopologyFolland, Real Analysis: Modern Techniques and Their Applications; Rudin, Functional Analysis; Royden, Real Analysis; Munkres, Topology.Tao, An Introduction to Measure Theory.
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Halmos, Naive Set Theory; Rudin, Real and Complex Analysis; Stein & Shakarchi, Real Analysis.
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203Asymptotic Analysis
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204ODELawrence Perko, Differential Equations and Dynamical Systems; Coddington & Levinson, Theory of Ordinary Differential Equations.
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206Banach Algebra; Spectral TheoryConway, A Course in Functional Analysis.
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208C*-AlgebrasDavidson, C*-Algebras by Example.
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214Differential ManifoldsSpivak, A Comprehensive Introduction to Differential Geometry.
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215A; 215BAlgebraic TopologyHatcher, Algebraic Topology; Milnor & Stasheff, Characteristic Classes.
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C218A; C218BDynamical Systems
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221Matrix ComputationsDemmel, Applied Numerical Linear Algebra; Trefethen & Bau, Numerical Linear Algebra.
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222A; 222BPDEEvans, Partial Differential Equations; Hormander, Analysis of Linear Partial Differential Operators.
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C223AStochastic Processes
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224AMathematical Methods; Physical SciencesRichtmyer, Principles of Advanced Mathematical Physics; Vaughn, Introduction to Mathematical Physics.
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225AMetamathematicsHodges, A Shorter Model Theory.
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227ARecursive Functions
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228A; 228BNumerical Solution; Differential Equations; ODE; PDELeveque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems; Iserles, A First Course in the Numerical Analysis of Differential Equations; Hairer, Norsett & Wanner, Solving Ordinary Differential Equations.
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229Model Theory
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235ASet Theory
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240Riemannian GeometryLee, Riemannian Manifolds:An Introduction to Curvature.
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241Complex ManifoldsForster, Lectures on Riemann Surfaces; Griffiths & Harris, Principles of Algebraic Geometry; Huybrechts, Complex Geometry: An Introduction.
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249Algebraic CombinatoricsStanley, Enumerative Combinatorics; Ziegler, Polytopes; Welsh, Matroid Theory.
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250AGroups; Rings; Fields; AlgebraLang, Algebra.
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250BMultilinear Algebra
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252Representation TheoryFulton & Harris, Representation Theory: A First Course; Curtis & Reiner, Representation Theory of Finite Groups and Associative Algebras.
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253Homological AlgebraCartan & Eilenberg, Homological Algebra; Weibel, An Introduction to Homological Algebra.
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254A; 254BNumber TheoryLang, Algebraic Number Theory; Neukirch, Algebraic Number Theory.Milne, Algebraic Number Theory
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Baker, Algebraic Number Theory Course Notes
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255Algebraic CurvesKirwan, Complex Algebraic Curves.
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256A; 256BAlgebraic GeometryHartshorne, Algebraic Geometry.
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261A; 261BLie GroupsFulton & Harris, Representation Theory: A First Course; Mark Sepanski, Compact Lie Groups.
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273Approximation Theory
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274AlgebraSilverman, The Arithmetic of Dynamical Systems; Milnor, Dynamics in One Complex Variable.
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275Applied Mathematics
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276Topology
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278Evans, Partial Differential Equations; Villani, Topics in Optimal Transportation.
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279PDE
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Stats 134Probability TheoryPitman, Probability.Ash, Basic Probability Theory.
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Stats 135Concepts of StatisticsRice, Mathematical Statistics and Data Analysis.
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Point-Set TopologyHatcher, Notes on Introductory Point-Set Topology; Morris, Topology Without Tears.Point Set Topology - Richard Southwell
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Measure TheoryTao, An Introduction to Measure Theory.
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Category Theory(Wikipedia pages)
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Tensor AnalysisBishop & Goldenberg, Tensor Analysis on Manifolds.
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AlgorithmCormen, Leiserson, Rivest & Stein, Introduction to Algorithms.
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Reading List
Copy of Reading List (Oct 18)