MATH MA Introduction to Functions and Calculus I 


Robin J. Gottlieb. Calculus: An Integrated Approach to Functions and Their Rates of Change, preliminary edition


MATH MB Introduction to Functions and Calculus II



MATH 1A Introduction to Calculus


Calculus: Concepts and Contexts, 4th edition, by James Stewart.


Schaum’s Outline of Precalculus, by Fred Safier


MATH 1B Calculus, Series, and Differential Equations



MATH 19A Modeling and Differential Equations for the Life Sciences


Clifford Taubes. Modeling Differential Equations in Biology, Prentice-Hall, Upper Saddle River, NJ, 2001.


MATH 19B Linear Algebra, Probability, and Statistics for the Life Sciences


Linear Algebra with Applications by Otto Bretscher


MATH 21A Multivariable Calculus


Multivariable Calculus: Concepts and Contexts, 4 book by James Stewart fourth edition


MATH 21B Linear Algebra and Differential Equations


Otto Bretscher,Linear Algebra, w,Applications, Editions 


MATH 23A Linear Algebra and Real Analysis I


Vector Calculus, Linear Algebra, and Differential Forms, Hubbard and Hubbard,fourth edition, Matrix Editions, 2009

Ross, Elementary Analysis: The Theory of Calculus, 2nd Edition, 2013.

Lawvere, Conceptual mathematics: a first introduction to categories, 2nd Edition,2009.

We will only be using the first chapter, and the book is available for free


MATH 23B Linear Algebra and Real Analysis II


Vector Calculus, Linear Algebra, and Differential Forms, Hubbard and Hubbard,fourth edition, Matrix Editions, 2009.


MATH 25A Honors Linear Algebra and Real Analysis I


Axler's Linear Algebra Done Right.

Spivak's Calculus.

Hoffman & Kunze's Linear Algebra.


MATH 25B Honors Linear Algebra and Real Analysis II


Simmons, G.F.: Introduction to Topology and Modern Analysis, McGraw-Hill 1963 

Edwards C.H.: Advanced Calculus of Several Variables, Dover 1994 (Academic Press 1973).


MATH 55A Honors Abstract Algebra


Axler's Linear Algebra Done Right.


Michael Artin’s Algebra.



MATH 55B Honors Real and Complex Analysis


Rudin W. Principles of Mathematical Analysis


MATH 101 Sets, Groups and Knots


Halmos, Naive Set Theory. Springer-Verlag, 1960.

Fraleigh, Abstract Algebra (7th ed.) Addison-Wesley, 2003.

Adams, The Knot Book. Amer. Math. Soc., 2001.


MATH 101 Sets, Groups and Topology


Paolo Aluffi, Algebra Chapter 0, Springer, Graduate Studies in Mathematics, 2009.

Paul R. Halmos, Naive Set Theory, Springer 1960.

Robert S. Wolf, Proof, Logic, and Conjecture: The Mathematician’s Toolbox, 1998.


MATH 110 Vector Space Methods for Differential Equations


Holland,Applied Analysis by the Hilbert Space Method (in the Coop) This

book starts from the beginning, with first-order linear differential equations.

Gerlach, Linear Mathematics in Infinite Dimensions


MATH 112 Introductory Real Analysis


Rudin W. Principles of Mathematical Analysis


MATH 113 Analysis I: Complex Function Theory


Elias M. Stein & Rami Shakarchi: Complex Analysis, Princeton University 2003


MATH 114 Analysis II: Measure, Integration and Banach Spaces


 ”Real Analysis” (4th edition) by Royden and Fitzpatrick.

Real Analysis: Measure Theory, Integration, and Hilbert Spaces by Elias M. Stein & Rami Shakarchi


MATH 115 Methods of Analysis


Dettman, John W. (John Warren). Mathematical methods in physics and engineering


Tang, K. T.. Mathematical methods for engineers and scientists.


MATH 116 Real Analysis, Convexity, and Optimization


Optimization by Vector Space Methods, Luenberger, Wiley, ISBN# 0471-18117-X


MATH 117 Probability and Random Processes with Economic Applications


Probability Theory in Finance, Sean Dineen,American Mathematical Scoiety, ISBN# 978-0-8218-3951-5.


MATH 118R Dynamical Systems


Introduction to Chaotic Dynamical Systems by Robert Devaney 


Dynamical Systems by Clark Robinson


Math 118 Notes by S. Sternberg and D. Goroff


A First Course in Dynamics, B. Hasselblatt and A. Katok, Cambridge University Press


MATH 121 Linear Algebra and Applications


Linear Algebra, 4th edition by Friedberg, Insel and Spence


MATH 122 Algebra I: Theory of Groups and Vector Spaces


Algebra by Michael Artin. This is the standard textbook one would use for this class. Provides a good collection of examples, exercises, and motivation.

Abstract Algebra by Dummit and Foote. This is a less expository, more formal textbook.

Undergraduate Algebra by Serge Lang.


MATH 123 Algebra II: Theory of Rings and Fields


Artin, Michael. Algebra 2nd edition. (2011)

Lang, Serge. Algebra. xv, 914 p. (c2002)


MATH 124 Number Theory


“The Higher Arithmetic: An Introduction to the Theory of Numbers” (Cambridge University Press; seventh edition) by H. Davenport.

Kato, Kurokawa, and Saito's Number Theory 1: Fermat's Dream.

Ireland, Kenneth F.. A classical introduction to modern number theory.


MATH 129 Number Fields


Samuel, Pierre. Algebraic theory of numbers


MATH 130 Classical Geometry


The Four Pillars of Geometry, John Stillwell


MATH 131 Topology I: Topological Spaces and the Fundamental Group


Topology by James R. Munkries


MATH 132 Topology II: Smooth Manifolds


Differential Topology, Guillemin & Pollack, AMS Chelsea Pub. (2010 Edition)

Calculus on Manifolds, Spivak

Topology from the Differentiable Viewpoint, Milnor

Differential Topology, Hirsch



MATH 136 Differential Geometry


do Carmo, Manfredo. Differential geometry of curves and surfaces

Kuhnel, Wolfgang. Differential geometry: curves - surfaces - manifolds. xii, 380 p. (c2006)


MATH 137 Algebraic Geometry


Griffiths, Phillip. Introduction to algebraic curves. x, 225 p. (1989)

Kirwan, Frances Clare. Complex algebraic curves. viii, 264 p. (1992


MATH 145A Set Theory I


Set Theory An Introduction To Independence Proofs, Kenneth Kunen

Jech’s Set Theory

Set Theory: The Independence Phenomenon(by Peter Koellner)


MATH 152 Discrete Mathematics


Discrete Mathematics,” Norman L. Biggs, second edition, Oxford University Press, 2002


MATH 153 Mathematical Biology-Evolutionary Dynamics


Nowak, M. A. (Martin A.). Evolutionary dynamics: exploring the equations of life. xi, 363 p. (2006)

Nowak, M. A.. Virus dynamics : mathematical principles of immunology and virology

Nowak, Martin. SuperCooperators.


MATH 154 Probability Theory


Probability and Random Processes ,

1000 Exercises in Probability.

Both books are by Geoffrey Grimmett and David Stirzaker, and both are published by

Oxford University Press. Get the third edition of Probability and Random Process. 


MATH 155R Combinatorics

‘A course in combinatorics’ by Van Lint and Wilson.


MATH 212A Real Analysis


Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Elias M. Stein & Rami Shakarchi

Partial Differential Equations: Second Edition, Lawrence C. Evans


MATH 212BR Advanced Real Analysis


Stein, Elias M.. Functional analysis: introduction to further topics in analysis.  (c2011)

Stein and Shakarchi. Fourier Analysis.

Stein, Elias M.. Real analysis: measure theory, integration, and Hilbert spaces. xix, 402 p. (c2005)


MATH 213A Complex Analysis


Stein and Shakarchi. Complex Analysis.

Whittaker, E. T. (Edmund Taylor). A course of modern analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions. 560 p. (2012)

Needham, Visual Complex Analysis. Oxford University Press, 1997.

Sansone and Gerretsen, Lectures on the Theory of Functions of a Complex Variable. (2 volumes.) P. Noordhoff, Ltd., 1960.

Serre, A Course in Arithmetic. Springer-Verlag, 1973.

Titchmarsh, Theory of Functions. Cambridge, 1939.


MATH 221 Algebra


Atiyah, MacDonald, Introduction to Commutative Algebra.

Fulton, Harris, Representation theory: A first course (selected topics from Chapters 7 - 10).

Eisenbud, Commutative Algebra with a view toward algebraic geometry.

Matsumura, Commutative ring theory


MATH 222 Lie Groups and Lie Algebras


The main textbook for this class is Lie groups: Beyond an Introduction, 2nd edition by

Anthony Knapp. The first edition of this book is available for free as a PDF through

SpringerLink. (http://link.springer.com/book/10.1007/978-1-4757-2453-0). The

main difference between the two editions is that the second edition adds a nice introductory

section on closed subgroups of linear groups. We’ll be covering material from

the chapters 1-5, and maybe some of chapter 6.

I will also be posting PDF course notes to the Canvas website after each class.

Other recommended books are:

Representation Theory by Fulton and Harris; this is one of the standard books on the

subject, and is extremely readable, with many examples. (SpringerLink URL: http:

//link.springer.com/book/10.1007/978-1-4757-2453-0.)

Compact Lie Groups by Sepanski: a good book at a less advanced level than Knapp;

particularly useful for the beginning of the course. (SpringerLink URL: http://link.

springer.com/book/10.1007/978-0-387-49158-5.)

Lectures on Lie Groups and Lie Algebras by Carter, Segal, and McDonald: the middle

section of this book is my favorite overview of Lie groups, and highly recommended as

supplementary reading. Not so much of a reference, as it is concise and requires you to

fill in the details, but gives a good sense of the big picture.

There are a vast number of online notes available from other courses on Lie theory.

Some I’d like to call to your attention are:

Kirillov’s notes: http://www.math.stonybrook.edu/~kirillov/mat552/liegroups.

pdf

(unofficial) Notes for a class taught by Sophie Morel at Princeton http://www-personal.

umich.edu/~zhufe1ng/mat449.pdf (notes by F1eng Zhu).

(unofficial) Notes for previous versions of this course: http://web.stanford.edu/

~tonyfe1ng/222.pdf (taught by Schmid, notes by Tony F1eng) and http://www.math.

harvard.edu/~amathew/224.pdf (taught by Harris, notes by Akhil Mathew).


MATH 224 Representations of Reductive Lie Groups


MATH 229X Introduction to Analytic Number Theory


Ram Murty, Problems in analytic number theory. (Has several exercises with solutions.)

Iwaniec, Kowalski, Analytic number theory. (Not required, and more advanced than needed. Excellent reference for more advanced material.)


MATH 230A Differential Geometry


Differential Geometry: Bundles, Connections, Metrics and Curvature? Clifford Taubes

Foundations of Differential Geometry? Shoshichi Kobayashi and Katsumi Nomizu


MATH 230BR Advanced Differential Geometry


Lawson, H. Blaine.. Spin geometry. xii, 427 p. (1989)


MATH 231A Algebraic Topology


Hatcher, Allen. Algebraic topology. xii, 544 p. : (2002)


MATH 231BR Advanced Algebraic Topology


Atiyah, Michael Francis. Collected works. 6 v. (c1988-2004)

Milnor, John Willard. Characteristic classes. v, 330 p. (1974)

Atiyah, Michael. Bott periodicity and the index of elliptic operators.

Atiyah, Michael. Bott periodicity and the parallelizability of the spheres.

Atiyah, Michael. Algebraic topology and operators in Hilbert space.


MATH 232A Introduction to Algebraic Geometry I


Harris, Joseph. Algebraic geometry : a first course. xix, 328 p. : (1992)

Shafarevich, I. R. (Igor? Rostislavovich). Basic algebraic geometry. 2 v. (2013)

Hartshorne , Robert. Algebraic Geometry.


MATH 232BR Algebraic Geometry II




MATH 233A Theory of Schemes I


The Geometry of Schemes, by Eisenbud and Harris. This is the main textbook for the

course, and focuses on concrete examples that can be visualized.


Algebraic Geometry and Arithmetic Curves, by Qing Liu. We will use this book as

reinforcement for the more algebraic and theoretical foundations of the subsject.


Optional supplementary texts for the course include


Foundations of Algebraic Geometry by Ravi Vakil, online course notes at: These notes

take a more categorical point of view


Algebraic Geometry by Robin Hartshorne is the standard book on the subject and an

excellent reference.



MATH 243 Evolutionary Dynamics


Evolutionary Dynamics, by Martin A. Nowak, and Evolutionary Games and Population Dynamics, by Josef Hofbauer and Karl Sigmund.


MATH 252 Linear Series and Positivity of Vector Bundles



MATH 256X Heisenberg Calculus in Quantum Topology



MATH 258Y Degenerations in Algebraic Geometry


MATH 260 Low Dimensional Topology: Mapping Class Groups 


MATH 263 Analytic Techniques in Algebraic Geometry


(GH) Griffiths-Harris: Principles of Algebraic Geometry

(Sz) Szekelyhidi: Introduction to Extremal metrics (PDF)

(P) Pho1ng: Course on Complex Analysis and Riemann Surfaces (notes by Qi You) (PDF)

(Gun) Gunning: Lectures on Riemann Surfaces

(Dem) Demailly: Complex analytic and differential geometry (PDF)

(Dem1) Demailly: Anaytic methods in algebraic geometry (PDF)

(Ber) Berndtsson: L2 methods for the dbar equation (PDF)

(Laz) Lazarsfeld: Positivity in Algebraic Geometry 1 and 2

(Bl) Blocki: Several Complex Variables ( PDF )

(Pa) Pa1un: Siu's invariance of plurigenera: A One-Tower proof ( PDF )


MATH 268Y Diophantine Approximation


MATH 274 Symplectic Duality


MATH 275X Topics in Geometry and Dynamics


M. B. Bekka and M. Mayer, Ergodic theory and topological dynamics of group actions on homogeneous spaces, Cambridge University Press, 2000.

Bekka, de la Harpe and Valette, Kazhdan's Property (T), 2007.

Benedetti and Petronio, Lectures on Hyperbolic Geometry, Springer-Verlag, 1992.

E. Ghys, Dynamique des flots unipotents sur les espaces homogenes, Sem. Bourbaki 1991/92; Asterisque 206.

M. Gromov, Volume and bounded cohomology

R. Mane, Ergodic Theory and Differentiable Dynamics

D. Witte Morris, Ratner's Theorems on Unipotent Flows, Chicago Lectures in Math. Series, 2005.

J. Ratcliffe, Foundations of Hyperbolic Manifolds, 2nd Edition. Springer, 2006.

W. P. Thurston, Three-dimensional Geometry and Topology, Princeton University Press, 1997.


MATH 283 Geometric Langlands Correspondence in Characteristic p


MATH 284X Canonical Bases in Representation Theory


MATH 286 Nonlinear Analysis in Geometry


MATH 288 Probability Theory and Stochastic Process 


MATH 300 Teaching Undergraduate Mathematics


MATH 303 Topics in Diophantine Problems Pasten Vasquez


MATH 304 Topics in Algebraic Topology Hopkins


MATH 308 Topics in Number Theory and Modular Forms Gross


MATH 314 Topics in Differential Geometry and Mathematical Physics Sternberg


MATH 316 Topics in Algebraic Geometry


MATH 318 Topics in Number Theory Mazur


MATH 321 Topics in Mathematical Physics Jaffe


MATH 327 Topics in Several Complex Variables Siu


MATH 333 Topics in Complex Analysis, Dynamics and Geometry McMullen


MATH 335 Topics in Differential Geometry and Analysis Taubes


MATH 343 Topics in Complex Geometry Collins


MATH 345 Topics in Geometry and Topology Kronheimer


MATH 346Y Topics in Analysis: Quantum Dynamics Yau


MATH 348 Topics in Representation Theory Haiden


MATH 352 Topics in Algebraic Number Theory Kisin


MATH 356 Topics in Harmonic Analysis Schmid


MATH 357 Topics in Model Theory Boney


MATH 361 Topics in Differential Geometry and Analysis Canzani


MATH 362 Topics in Number Theory Miller


MATH 364 Topics in Algebraic Geometry Ullery


MATH 365 Topics in Differential Geometry S.T. Yau


MATH 368 Topics in Algebraic Topology Peterson


MATH 373 Topics in Algebraic Topology Lurie


MATH 381 Introduction to Geometric Representation Theory Gaitsgory


MATH 382 Topics in Algebraic Geometry Harris


MATH 385 Topics in Set Theory Woodin


MATH 387 Topics in Mathematical Physics: Bridgeland Stability Conditions Tanaka


MATH 388 Topics in Mathematics and Biology Nowak


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