MathBookRecommendations.md

Math Book Recommendations

Here I've recorded some math books that I found the most useful for learning a particular topic, inspired by the "Chicago Undergraduate Mathematics Bibliography" (https://www.ocf.berkeley.edu/~abhishek/chicmath.htm), which I found very useful during my undergraduate years:

An ! before the title of a book is used to indicate a book I have only read a small portion of, but which I found useful enough to write down in case I ever need to read further into a particular field.

Fundamentals

Linear Algebra

• • Carl Meyer, Matrix Analysis and Applied Linear Algebra

    Looks like a good book for studying basic matrix algebra.

• Charles Curtis, Linear Algebra: An Introductory Approach

  The First Linear Algebra Book I read. Does the job of teaching the basic ideas, without too much flair or extras.

• Paul Halmos, Finite-Dimensional Vector Spaces

  Utilizes the modern terminology and techniques of functional analysis on infinite dimensional vector spaces to the finite dimensional. Suprisingly, this modern approach makes the material very readable.

• Stephen Friedberg / Arnold Insel / Lawrence Spence, Linear Algebra

  Pretty bog standard linear algebra book. Gets through all the potential topics you need.

• Peter Lax, Linear Algebra and its Applications

  An advanced book on finite dimensional linear algebra and matrix theory. Most people skip these parts of linear algebra, but there are very important uses for this theory! Not all linear algebra is functional analysis in disguise. Read this for concreteness!

• ! Denis Serre, Matrices

• ! Rajendra Bhatia, Positive Definite Matrices

Discrete Mathematics

• Ronald Graham / Donald Knuth / Oren Patashnik, Concrete Mathematics: A Foundation for Computing Science

  A problems book designed so that computing science students can read Donald Knuth's monolithic "The Art of Computer Programming" series. However, it really is a good introduction to the basic ideas of discrete mathematics, solving recurrences, basic number theory, generating functions, discrete probablity theory, and asymptotics. Very useful, and you'll likely learn techniques you didn't know if you read it, even if you think you already know all the discrete mathematics you will need.

• John Michael Steele, The Cauchy Schwartz Master Class

• ! Gowers, Techniques in Combinatorics

Calculus & Introductory Analysis

• Walter Rudin, Principles of Mathematical Analysis

  Very terse text in basic analysis.

• Michael Spivak, Calculus

  Less terse text in basic analysis.

• Thomas Korner, A Companion to Analysis

  Great supplement to a basic analysis course. Explains 'why' basic analysis isn't so intuitive as you might believe.

• Hermann Schey, Div, Grad, Curl, and all that

  Great introduction to classical vector calculus.

• Michael Spivak, Calculus on Manifolds

  Covers basic multivariate calculus, and elementary differential forms / integration on manifolds.

• ! Robert S. Strichartz, The Way of Analysis

• ! Richard Courant, Introduction To Calculus and Analysis, Vol 1 + 2.

• ! Otto Toeplitz, Calculus: a Genetic Approach

• ! Abbott, Understanding Analysis

• ! Peter D. Lax and Maria Shea Terrell, Multivariate Calculus With Applications.

Basic Probability Theory

• Larry Wasserman, All of Statistics: A Concise Course in Statistical Inference

• William Feller, An Introduction to Probability Theory and its Applications (Vol 1-2)

• ! David Williams, Weighing the Odds: A Course in Probability Theory

Geometry

• ! Robin Hartshorne, Geometry: Euclid and Beyond

• ! Jurgen Richter-Gebert, Perspectives on Projective Geometry

• ! Keith Carne, University of Cambridge Lecture Notes, Geometry and Groups

• ! Hermann Weyl, Symmetry

• ! Oliver Byrne, The First Six Books of The Elements of Euclid.

• ! Cecil, Lie Sphere Geometry

• ! Carne, Geometry and Groups

• ! Benz, Geometry of Real Inner Product Spaces

• ! Hartshorne, Projective Geometry

• ! Oggier / Bruckstein, Groups and Symmetries

• ! Coxeter, the Real Projective Plane

Complex Analysis / Harmonic Functions

• Elias Stein / Rami Shakarchi, Princeton Lectures in Analysis (Vol 2: Complex Analysis)

• Lars Ahlfors, Complex Analysis

• ! Garnett, Bounded Analytic Functions

Classical Differential Geometry

• ! Manfredo do Carmo, Differential Geometry of Curves and Surfaces

• ! Sharpe, Differential Geometry: Cartan's Generalization of Klein's Erlangen Program

• ! Shifrin, Differential Geometry: A First Course in Curves and Surfaces

Differential Equations

• Vladimir Arnold, Ordinary Differential Equations

  A much more 'practical' differential equations book. Talks about the actual geometrical theory behind differential equations, and an introduction to the more 'chaotic aspects' relating differential equations to dynamical systems. Choose this if you want a differential equations course that is actually interesting! The second edition republishing by Springer includes many real-word examples of differential equation (logistic equation, Lotka-Volterra, etc) which add variety to the exposition

• ! Steven H. Strogatz, Nonlinear Dynamics and Chaos

• ! Garrett Birkhoff / Gian-Carlo Rota, Ordinary Differential Equations

• ! John Guckenheimer / Philip Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields.

Mathematical Physics

• Lev Landau / Evegeny Lifshitz, Course of Theoretical Physics:

• Michael Spivak, Physics for Mathematicians

• ! Ain Sonin, Dimensional Analysis

• S Cornbleet, Geometrical Optics Reviewed: A New Light on an Old Subject.

Advanced Topics

Abstract Algebra

• Kostrikin / Shafarevich, Algebra I: Basic Notions

  Introduces the general fields of abstract algebra (Groups, rings, modules, etc) as a natural extension of certain practical problems that arise in fields of mathematics. I only read this book after I already knew about all these structures, but the book really made them 'fit' in my mind with respect to the general field of mathematics. I am very interested in how successful an 'algebra' course would be if it introduced the field of abstract algebra as a consolidated whole like this book tries to accomplish.

• Serge Lang, Algebra

  Terse but thorough. I suggest reading it along with G. Bergman's companion to the book.

• Michael Artin, Algebra

  Tries to use more 'matrix / linear algebra' knowledge to build up a knowledge of basic algebra.

• Dummett / Foote, Algebra

• ! Eisenbud, Commutative Algebra

• ! Gathman, Commutative Algebra

• ! Clark, Commutative Algebra

• ! Maclane, Category Theory

• ! Lawvere, Conceptual Mathematics

• ! Milnor, Algebraic K-Theory

• ! Wiebel, The K-Book

Topology

• John Kelley, General Topology

• James Munkres, Topology

• ! Viro / Ivanov / Netsvetaev / Kharlamov, Elementary Topology: Problem Textbook

Galois Theory

• James Stewart, Galois Theory

• Nathan Jacobson, Basic Algebra I (Section on Galois Theory)

Algebraic Topology

• Allen Hatcher, Algebraic Topology

• ! John Stillwell, Classical Topology and Combinatorial Group Theory

  Gives geometry inspiration for the basic concepts of algebraic topology: fundamental groups and homology theory.

Measure Theory

• Walter Rudin, Real and Complex analysis

  One of the best and most concise introductions to measure theory I've read. The first chapter essentially includes all the big theorems of measure theory you'll need, and the next few chapters include the other little important things that are useful (product measures, radon nikodym derivates, etc). Also includes a strange second part on complex analysis that I haven't got round to reading, but apparently proceeds by an incredible strange approach.

• Terrence Tao, An Introduction to Measure Theory

  Very good for building intuition.

• Elias Stein / Rami Shakarchi, Princeton Lectures in Analysis (Vol 3: Measure Theory, Integration and Hilbert Spaces)

• Paul Halmos, Measure Theory

Functional Analysis

• Elias Stein / Rami Shakarchi, Princeton Lectures in Analysis (Vol 4: Functional Analysis)

• ! Paul Halmos, A Hilbert Space Problem Book

• John Conway, A Course in Functional Analysis

• Peter Lax, Functional Analysis

  Really good for applications of functional analysis, giving motivations for the study of functional analysis rather than just the abstract theory.

• Robert Megginson, An Introduction to Banach Space Theory

• Francois Treves, Topological Vector Spaces, Distributions, and Kernels

• Walter Rudin, Functional Analysis

• ! Fabian, Habala, Hajek, Montesinos, Zivler, Banach Space Theory

  Incredibly comprehensive book on the advanced areas of Banach space

• ! Joseph Diestel / John Uhl Jr. Vector Measures

  Good resource for learning vector valued integration theory.

• ! Patrick Billingsley, Convergence of Probability Measures

Modern Differential Geometry

• Michael Spivak, A Concise Introduction to Differential Geometry (Vol 1-5)

• Frederic Schuller, A Thorough Introduction To The Theory of General Relativity (International Winter School on Gravity and Light 2015)

  Lecture 1 (Topology): https://www.youtube.com/watch?v=7G4SqIboeig

  Lecture 2 (Topological Manifolds): https://www.youtube.com/watch?v=93f-ayezCqE

  Lecture 3 (Multilinear Algebra): https://www.youtube.com/watch?v=mbv3T15nWq0

  Lecture 4 (Differentiable Manifolds): https://www.youtube.com/watch?v=HSyTEwS4g80

  Lecture 5 (Tangent Spaces): https://www.youtube.com/watch?v=pepU_7NJSGM&spfreload=10

  Lecture 6 (Fields): https://www.youtube.com/watch?v=UbQS40KHkH0

  Lecture 7 (Connections): https://www.youtube.com/watch?v=nEaiZBbCVtI

  Lecture 8 (Parallel Transport and Curvature): https://www.youtube.com/watch?v=2eVWUdcI2ho

  Lecture 9 (Newtonian Spacetime is Curved): https://www.youtube.com/watch?v=IBlCu1zgD4Y

  Lecture 10 (Metric Manifolds): https://www.youtube.com/watch?v=ONCZNwKswn4

  Lecture 11 (Symmetry): https://www.youtube.com/watch?v=v4jolM-bPpA

  Lecture 12 (Integration on Manifolds): https://www.youtube.com/watch?v=2XpnbvPy-Zg

  (It gets more physicsy after this, but this is still interesting, especially since it motivated quite a bit of modern differential geometry to begin with)

  Despite it's name, this lectures series is an introduction to the basic ideas of differentiable manifolds, with the goal of introducing them to theoretical physicists. Based on your experience, you can probably skip some of these lectures, but they proceed at a very gradual pace and introduce all the essentials to manifold theory. While I was studying the basic properties of differential geometry, they made a nice complement to Volume 1 of Spivaks' differential geometry introduction, and Lees introduction to smooth manifolds.

• John Lee, Introduction to Smooth Manifolds

  I found this book a little bit more concise than Spivaks book, which helped make some concepts more readable. But I still think both should be read for a true understanding of differential geometry.

• ! Tu, Differential Geometry: Connections, Curvature, and Characteristic Classes

• ! Needham, Visual Differential Geometry and Forms, A Mathematical Drama in Five Acts

• ! Serge Lang, Fundamentals of Differential Geometry

  In true, abstract Serge Lang style, the book introduces the usual theory of differentiable manifolds as a theory of spaces that look locally like infinite dimensional Banach spaces. If you like Serge Lang books, you'll like this one.

• ! Marian Fecko, Differential Geometry for Physicists

• ! Morris Herch, Differentiable Topology

Partial Differential Equations

• ! Craig Evans, Partial Differential Equations

• ! Vladimir Arnold, Lectures on Partial Differential Equations

• ! Axler, Harmonic Function Theory

• ! Korner, Partial Differential Equations Notes

• ! Taylor, Partial Differential Equuations

• ! Ambrosio / Gigli, A User's Guide to Optimal Transport

• ! Zeidler, Nonlinear Functional Analysis and Its Applications (4 Volumes)

Commutative Algebra

• Atiyah Macdonald, Commutative Algebra

• ! Pete L. Clark, Commutative Algebra

Algebraic Geometry

• ! Beltrametti, Lectures on Curves, Surfaces, and Projective Varieties

• Brieskorn Knorrer, Plane Algebraic Curves

  Read for Culture

• William Fulton, Algebraic Curves

• ! Gerd Fischer, Plane Algebraic Curves

  Very elementary for what is proven. Useful for a first introduction.

• ! Igor Shaferavich, Basic Algebraic Geometry I

• ! Liu, Algebraic Geometry and Arithmetic Curves

• ! Harris, Geometry of Schemes

• ! Harris, Algebraic Geometry

• ! Gathman, Algebraic Geometry

• ! Robin Hartshorne, Algebraic Geometry

• ! Lie, Algebraic Geometry

• ! Cox, Toric Varieties

• ! Dolgachov, Classical Algebraic Geometry: A Modern View

Mathematical Logic

• Chiswell / Hodges, Mathematical Logic

  Good intro to someone who hasn't had any 'real' mathematical logic yet.

• Mendelson, Introduction to Mathematical Logic

• ! Jech, Set Theory

• ! Dirk Van Dalen, Logic and Structure

Theoretical Computing Science

• Michael Sipser, Introduction to the Theory of Computation

  The standard introduction to models of computation. Starts off with the basic forms of computation, including introductions to pushdown automata and grammars, but quickly moves onto computability in Turing machines. An interesting feature of this book is that each big proof is preceded by a 'proof idea' section, which explains the idea behind the more technical parts of the proof you're about to read. This is really useful, and this technique should be used in more basic introductions to mathematical subjects. The only weakness of this book is that it doesn't include the parts of computation theory that connect to mathematical logic, which I have yet to find a good resource for yet.

• ! Boaz Barak, Introduction to Theoretical Computing Science

• ! Sanjeev Arora and Boaz Barak, Computational Complexity: A Modern Approach

  Yes. There is a whole diverse theory of computational complexity which goes beyond 'Does P = NP'. This is THE book for this topic, and includes a range of different advanced subjects going beyond the basic complexity classes encountered in an introductory course in a theory of computation. I haven't had a chance to read it throughly, but the special topics I have read into (probabilistically checkable proofs and the PCP theorem) were well put together.

Number Theory

• ! Godfrey Hardy, Number Theory

• ! Oggier, Algebraic Number Theory

• ! Chandresekheran, Analytic Number Theory

• ! Davenport, Multiplicative Number Theory

• ! Allen Hatcher, the Topology of Numbers

• ! Hugh Montgomery / Robert Vaughan, Analytical Number Theory

• ! Hugh Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis

• ! Terence Tao, Analytical Number Theory Online Notes

• ! Baker, An Introduction to p-adic Numbers and p-adic Analysis

Representation Theory

• ! William Fulton / Joe Harris, Representation Theory

Operator Algebras / Operator Theory

• John Conway, A Course in Functional Analysis

• Kadison / Ringrose, Fundamental of the Theory of Operator Algebras

• Kenneth Davidson, C^* Algebras by Example

• ! Davies, Spectral Theory and Differential Operators

• ! Milivoje Lukic. A First Course in Spectral Theory.

• ! McIntosh, Operator Theory - Spectra and Functional Calculi

• ! Hytonen, Neervan, Veraar, Weis - Analysis in Banach Spaces: Probabilistic Methods

Abstract Harmonic Analysus

• Gerald B. Folland, A Course in Abstract Harmonic Analysis

• Walter Rudin, Fourier Analysis on Groups

  An introduction to only the abelian aspects of abstract harmonic analysis. A good complement to Follands book, which focuses on aspects of the theory important to the noncommutative theory.

• !Edwin Hewitt, Kenneth Ross, Abstract Harmonic Analysis (Vol 1-2)

  Incredibly comprehensive, but so slow going I can't recommend it for a first introduction.

Ergodic Theory

• ! Manfred Einsiedler / Thomas Ward, Ergodic Theory With a View Towards Number Theory

Special Topics in Discrete Mathematics

• ! Herbert Wilf, Generatingfunctionology

• Larry Guth, Polynomial Methods in Combinatorics

• Ryan O' Donnell, Analysis of Boolean Functions

• ! Kahane, Some Random Series of Functions

• ! Alon, Spencer, The Probabilistic Method

• ! Terrence Tao, Additive Combinatorics

• ! Stanley, Enumerative Combinatorics

• ! Bondy, Graph Theory

Optimization

• Chvatal, Linear Optimization

• Bertsimas, Tsitsiklis, Introduction to Linear Optimzation

• ! Bubeck, Convex Optimization

• ! Weber, Optimization

Modular Forms

• ! Jan Hendrik Bruiner / Gerad van der Geer / Gunter Harder / Don Zagier, The 1-2-3 of Modular Forms

  This was the book that really attracted me to the theory of modular forms and their applications. Unlike other books, which focus specifically on the theory without introducing applications, this book introduces the applications while introducing the theory, which makes the path to understanding modular forms much more visceral.

• ! Don Zagier Lectures in Modular Forms

  Lecture 1: https://www.youtube.com/watch?v=zKt5L0ggZ3o

  Lecture 2: https://www.youtube.com/watch?v=FVje_MN8SUE

  Lecture 3: https://www.youtube.com/watch?v=uFaX8eNn64A

  Lecture 4: https://www.youtube.com/watch?v=jpanciocK4Y

  Lecture 5: https://www.youtube.com/watch?v=JwWOH9ty9b0

  Really good introduction to Modular forms, from the view of theoretical physics (but still a useful introduction for mathematicians!).

• Fred Diamond / Jerry Shurman, A First Course in Modular Forms

  This book introduces the Riemann surface theory which connects to Modular forms, which helped me understand some of the technical aspects of the theory, and its generalizations to the theory of automorphic forms. Maybe if you read a better resource on general Riemann surfaces this is unneccessary, and I might find this book not so useful once I know Rieman surface theory, but for now it's still very useful.

• Neal Koblitz, Introduction to Elliptic Curves and Modular Forms

• ! J.S. Milne, Modular Functions and Elliptic Curves

• ! William Stein, Modular Forms: A Computational Approach

• ! Bringmann, Folsom, Ono, Rolen. Harmonic Maass Forms and Mock Modular Forms: Theory and Applications.

Lie Algebras and Groups

• Karin Erdmann / Mark J. Wildon, Introduction to Lie Algebras

• Varadarajan, Lie groups Lie Algebras and Their Representations

• Brian Hall, Lie Groups Lie Algebras and Representation Theory

• ! Mazorchuk, Lectures on SL_2(C) modules

• Alistair Savage, Introduction to Lie Groups

Lambda Calculus / Theories of Computation

• Hindley / Selden: Lambda Calculus and Combinators

• Raymond Smullyan, To Mock a Mockingbird and Other Logic Puzzles

• Ulf Nillson / Jan Maluszynski, Logic Programming and Prolog.

Riemann Surfaces / Several Complex Variables

• ! Jurgen Jost, Compact Riemann Surfaces

• ! Robert Gunning, Lectures on Riemann Surfaces

• ! Huybrecht, Complex Geometry

• ! Krantz, A Handbook of Complex Variables

• ! Robert Gunning. Analytic Functions of Several Complex Variables.

Symplectic Geometry

• ! Yong-Geun Oh, Symplectic Topology and Floer Homology

Topics in Probability Theory

Stochastic Processes

• Lawler, Introduction to Stochastic Processes

• ! David Levin / Yuval Peres / Elizabeth Wilmer, Markov Chains and Mixing Times

• ! Jean Francois Le Gall, Brownian Motion, Martingales, and Stochastic Calculus

• ! Theodore Harris, The Theory of Branching Processes

• ! Atherya / Ney, Branching Processes

• ! Nils Berglund, Long-Time Dynamics of Stochastic Differential Equations

• ! Daley / Vere-Jones, An Introduction To The Theory of Point Processes

• ! Keeler, Notes on the Poisson Point Process

• ! Johnson, Introduction to Spatial Point Processes

• ! Michael Kozdron, Lectures on Stochastic Calculus with Applications to Finance

• ! Miller, Stochastic Calculus

• ! Ramon Van Handel, Stochastic Filtering and Control

High Dimensional Probability Theory

• ! Terence Tao, Topics in Random Matrix Theory

• Ramon van Handel, Probability in High Dimension Lecture Notes

• Roman Vershynin, High Dimensional Probability

• ! Stephane Boucheron / Gabor Lugosi / Pascal Massart, Concentration Inequalities: A Nonasymptotic Theory of Independence

• ! Martin Wainwright, High-Dimensional Statistics

• ! Remi Rhodes / Vincent Vargas, Lectures on Gaussian Multiplicative Chaos

Integrable Probability

• ! Alexei Borodin / Vadim Gorin Integrable Probability

Mathematical Statistics

• ! Hastie, Tibshirani, Friedman, the Elements of Statistical Learning

• Tor Lattimore and Csaba Szepesvari, Bandit Algorithms

• ! Shervish, Mathematical Statistics

Information Theory

• ! Stephen Barnett, Introduction to Quantum Information

• ! Simon DeDeo, Information Theory for Intelligent People

• ! John Watrous, The Theory of Quantum Information

Geometric Probability Theory (Percolation + Gaussian Free Fields)

• ! Russell Lyons / Yuval Peres, Probability on Trees and Networks

• ! Nathenael Berestycki / Ellen Powell, Gaussian Free Field, Liouville Quantum Gravity, and Gaussian Multiplicative Chaos

Harmonic Analysis / Geometric Measure Theory

Fourier Series / General Books on Fourier Analysis

• Elias Stein / Rami Shakarchi, Fourier Analysis

• T.W. Korner, Fourier Analysis (Plus Exercise Book)

• Steven Krantz, A Panorama of Harmonic Analysis

• Javier Duoandioketxea, Fourier Analysis

• Stein, Weiss, Fourier Analysis on Euclidean Spaces

• Thomas Wolff, Lectures on Harmonic Analysis

• Terence Tao, Lecture notes for Math 247A: Harmonic Analysis

• ! Elias Stein, Singular Integrals

• ! Deng, Han, Harmonic Analysis on Spaces of Homogeneous Type.

• ! Grafakos, Classical + Modern Harmonic Analysis

• Elias Stein, Harmonic Analysis

• ! R.E. Edwards: Fourier Series Volumes One and Two

• ! Breen, Harmonic Analysis Notes

• ! Bremeaut, Fourier Analysis And Stochastic Processes

• ! Atelier d'Analyse Harmonique 2019, Littlewood-Paley Theory and Applications

• Katznelson, An Introduction to Harmonic Analysis

• ! Osgood, Lectures on the Fourier Transform

• ! Zygmund Trigonometric Series

• ! Muscalu / Schlag, Classical and Multilinear Harmonic Analysis

Complex Analysis and Harmonic Analysis

• ! Havin, Introduction to Hp Spaces

Interpolation Theory

• ! Tartar, Interpolation Spaces

• ! Bergh, Interpolation Spaces

• ! Brudnyi / Krugljak, Interpolation Functors and Interpolation Spaces

• ! Triebel, Interpolation Spaces

PDOs / Fourier Integral Operators / Riemannian Harmonic Analysis

• ! Zelditch Notes

• ! Rosenberg, the Laplacian on a Riemannian Manifold

• ! Zanelli, Lectures on Fourier Integral Operators: From Local to Global Theory

• Hormander, Vol 1-4

• ! Sogge, Fourier Integrals in Classical Analysis

• ! Sogge, Hangzhou Lectures on Eigenfunctions of the Laplacian

• ! Brain Street, Maximal Subellipticity

• ! Tataru, Microlocal Analysis

• ! Taylor, Pseudodifferential Operators

• Treves Vol 1 + 2

Time Frequency Analysis

• ! Folland, Harmonic Analysis in Phase Space

Semi-Classical Analysis

• ! Zworski, Semiclassical Analysis

• ! Guillemin / Sternberg, Semi-Classical Analysis

Symmetric Spaces

• ! Helgason, Lie Groups and Symmetric Spaces

Restriction Theory

• ! Terence Tao, Notes from Restriction Theory

• ! Ciprian Demeter, Restriction and Decoupling

• ! Johnathan Hickamn, Modern Developments in Fourier Analysis Notes

Geometric Measure Theory

• Kenneth Falconer, Fractal Geometry: Mathematical Foundations and Applications

• Kenneth Falconer, The Geometry of Fractal Sets

• Pertti Mattila, Geometry of Sets and Measures in Euclidean Space

• Pertti Mattila, Fourier Analysis and Hausdorff Dimension

• Frederick Almgren Jr., Plateau's Problem: An Introduction to Varifold Geometry

• ! Frank Morgan, Introduction to Geometric Measure Theory

• ! Herbert Federer, Geoemtric Measure Theory

• T.W. Korner, Baire Categorry, Probabilistic Constructions, and Convolution Squares

  Gives a detailed account of many uses of using the Baire category theorem to construct pathologic sets in analysis.

Signals Processing / Physical Intuition

• ! Vetterli / Kovacevic / Goyal, Foundations of Signal Processing

• ! Lyons, Digital Signal Processing

• ! Oppenheimer, Discrete-Time Signal Processing

• ! Oppenheimer, Signals and Systems

• ! Byrne, Signals Processing: A Mathematical Approach

Expository Articles

• ! (Many Authors): Analysis and Applications: The Mathematical Work of Elias Stein

• Scott Miller, Review of Mumford Algebraic Geometry Book

  Good for intuition / history about the development of scheme theory

• Andreas Seeger, Review of Fourier Restriction on Paraboloid

• Gregory Moore, The emergence of closed and open sets in analysis

• G.G Lorentz, Who Discovered Analytic Sets

• Issacc Goldbring and Sean Walsh, An Invitation to Nonstandard Analysis

• ! Terrence Tao: An Epsilon of Room / Spending Symmetry / etc (Multiple Volumes)

• Hiller, Crystallography and Cohomology of Groups

• Krantz, Mathematical Apocrypha

• Krantz, Advice

• Krantz, Primer for Mathematical Writing