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Introduction to Philosophy (Optional but Recommended):

Think: A Compelling Introduction to Philosophy Simon Blackburn

Philosophy: A Text with Readings Manuel Velasquez

Thinking It Through: An Introduction to Contemporary Philosophy Kwame Appiah


Introduction to Logic (Optional but Recommended):

The Power of Logic Frances Howard-Snyder, Daniel Howard-Snyder, Ryan Wasserman

A Concise Introduction to Logic Patrick J. Hurely


Precalculus :

Precalculus: Mathematics for Calculus James Stewart, Lothar Redlin, Saleem Watson

Precalculus Michael Sullivan


Calculus :

Calculus: Early Transcendentals James Stewart

Infinite Powers: How Calculus Reveals the Secrets of the Universe Steven H. Strogatz (Optional but Recommended).

Thomas' Calculus George B. Thomas, Jr.


Problem Solving (Optional but Recommended):

How to Solve It G. Polya

Solving Mathematical Problems Terence Tao

How to Solve Mathematical Problems Wayne Wickelgren

Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving, George Polya


Introduction to Physics (Optional):

Physics for Scientists and Engineers with Modern Physics Raymond A. Serway, John W. Jewett Jr.

An Introduction to Physical Science James T. Shipman, Jerry D. Wilson, Charles A. Higgens Jr.

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics Randall D. Knight


Introduction to Linear Algebra :

Elementary Linear Algebra Howard Anton, Chris Rorres

Introduction to Linear Algebra Gilbert Strang

Linear Algebra and Its Applications David C. Lay, Steven R. Lay, Judi J. McDonald


Introduction to Differential Equations :

Elementary Differential Equations and Boundary Value Problems William E. Boyce, Richard C. DiPrima

Differential Equations Dennis Zill, Warren Wright

Fundamentals of Differential Equations David Snider, Edward B. Saff, and R. Kent Nagle


Introduction to Partial Differential Equations :

Partial Differential Equations for Scientists and Engineers Stanley J. Farlow

Linear Partial Differential Equations Tyn Myint-U & Lokenath Debanath

Partial Differential Equations An Introduction Walter A. Strauss

Partial Differential Equations Mark A. Pinsky


Naive Set Theory, Mathematical Reasoning, Proofs:

How to Prove It Daniel J. Velleman

Introduction to Mathematical Proofs Charles E. Roberts

Book Of Proof Richard Hammak

Proofs and Fundamentals Ethan D. Bloch


Discrete Mathematics :

Discrete Mathematics with Applications Susanna S. Epp

Discrete Mathematics and Its Applications Kenneth H. Rosen

Mathematics: A Discrete Introduction Edward R. Scheinerman


Introduction to Axiomatic Set Theory :

Classic Set Theory Derek Goldrei

Introduction to Set Theory Karel Hrbacek, Thomas Jech

Elements of Set Theory Herbert Enderton

Foundations of Set Theory A.A. Fraenkel. Y. Bar-Hillel, A. Levy

A First Course in Mathematical Logic and Set Theory Michael L. O'Leary


Introduction to Mathematical Logic and Model Theory :

Mathematical Logic Ian Chiswell, Wilfrid Hodges

A Mathematical Introduction to Logic Herbert Enderton

A First Course in Logic Shawn Hedman

Propositional and Predicate Calculus Derek Godrei

A Friendly Introduction to Mathematical Logic Christopher C. Leary

Introduction to Mathematical Logic Elliott Mendelson


Introduction to the Theory of Computation :

Introduction to the Theory of Computation Michael Sipser

Computability Theory Herbert Enderton

Introduction to Languages and the Theory of Computation John C. Martin


Introduction to Lattice Theory :

Lattices and Ordered Sets Steven Roman

Introduction to Lattices and Order B.A. Davey


Universal Algebra :

Universal Algebra P.M. Cohn

An Invitation to General Algebra and Universal Constructions George M. Bergman

Universal Algebra G. Gratzer

A Course in Universal Algebra Stanley Burris, H.P. Sankappanavar

Universal Algebra Clifford Bergman

Post-Modern Algebra Jonathan D. H. Smith, Anna B. Romanowska


Introduction to Combinatorics :

Combinatorial Reasoning: An Introduction to the Art of Counting Duane DeTemple, William Webb

Introductory Combinatorics Richard A. Brualdi

Combinatorics: An Introduction Theodore G. Faticoni

How to Count: An Introduction to Combinatorics and Its Applications Robert A. Beeler


Introduction to Probability Theory :

introduction to Probability Dimitri Berstekas, John N. Tsitsiklis

A First Course in Probability Theory Sheldon Ross

A Natural Introduction to Probability R. Meester

Introduction to Probability Joseph K. Blitzstein, Jessica Hwang


Introduction to Game Theory :

Game Theory Steven Tadelis

Strategy Joel Watson

Game Theory: A Critical Introduction Shaun P. Hargreaves Heap, Yanis Varoufakis

Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction Herbert Gintis


Introduction to Mathematical Statistics :

Introduction to Probability and Mathematical Statistics Lee J. Bain, Max Engelhardt

An Introduction to Mathematical Statistics and Its Applications Richard Larsen, Morris Marx

Mathematical Statistics with Applications Dennis D. Wackerly, William Mendenhall, Richard L. Scheaffer

Introduction to Mathematical Statistics Robert V. Hogg, Joseph W. McKean, Allen T. Craig

A Modern Introduction to Probability and Statistics: Understanding Why and How F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester

Modern Mathematical Statistics with Applications Jay L. Devore, Kenneth N. Berk


Advanced Probability Theory :

An Introduction to Probability and Statistics V. K. Rohatgi, A. K. Md. E. Saleh

A First Look at Rigorous Probability Theory Jeffrey S. Rosenthal

A User's Guide to Measure Theoretic Probability David Pollard

An Introduction to Probability Theory and Its Applications William Feller

Probability and Measure Patrick Billingsley

Probability A. N. Shiryayev


Advanced Mathematical Statistics :

Statistical Inference George Casella, Roger L. Berger

Mathematical Statistics: Basic Ideas and Selected Topics Kjell A. Doksum, Peter J. Bickel

Theory of Statistics Mark J. Schervish

Robust Statistics Frank  R. H., Elvezio M. R., Peter J. R., Werner A. S.

All of Statistics Larry Wasserman

All of Nonparametric Statistics Larry Wasserman


Introduction to Real Analysis:

Introduction to Real Analysis Robert G. Bartle, Donald R. Sherbert

Introduction to Real Analysis William F. Trench

How to Think About Analysis Lara Alcock

From Calculus to Analysis Steen Pedersen

Writing Proofs in Analysis Jonathan M. Kane


Introduction to Numerical Analysis :

Numerical Analysis Timothy Sauer

Numerical Analysis Richard Burden Jr. Douglas Faires

Numerical Methods That Usually Work Forman S. Acton

An Introduction to Numerical Methods and Analysis James F. Epperson


Introduction to General Topology :

General Topology Stephen Willard

First Concepts of Topology W. G. Chinn & N. E. Steenrod

Topological Spaces Gerard Buskes, Arnoud van Rooij

Topology Without Tears Sidney A. Morris

Introduction to Metric and Topological Spaces Wilson A. Sutherland

Topology James Munkres


Introduction to Mathematical Analysis :

Principles of Mathematical Analysis Walter Rudin

The Elements of Real Analysis Robert G. Bartle

Mathematical Analysis Tom Apostol

Methods of Real Analysis Richard R. Goldberg

Advanced Calculus of Several Variables C. H. Edwards Jr.

Calculus and Analysis in Euclidean Space Jerry Shurman


Introduction to Optimization Theory :

A First Course in Optimization Theory Rangarajan K. Sundaram

Introduction to Linear Optimization Dimitris Bertsimas. John N. Tsitsiklis

Applied Optimization Ross Baldick

Practical Optimization Philip E. Gill, Walter Murray, Margaret H. Wright

An Introduction to Optimization Edwin K.P. Chong, Stanislaw H. Zak


Convex Optimization :

Convex Optimization Theory Dimitri P. Bertsekas

Convex Optimization Stephen Boyd, Lieven Vandenberghe

Convex Analysis and Nonlinear Optimization Jonathan M. Borwein, Adrian S. Lewis

Foundations of Optimization Osman Güler


Introduction to Differential Geometry :

A Differential Approach to Geometry Francis Borceux

Differential Geometry of Curves and Surfaces Kristopher Tapp

Differential Geometery of Curves and Surfaces Manfredo P. Do Carmo

Elementary Differential Geometry Barrett O'Neill

Elementary Differential Geometry Andrew Pressley


Advanced Differential Geometry :

Manifolds, Tensors and Forms Paul Renteln

An Introduction to Differentiable Manifolds and Riemannian Geometry William M. Boothby

Introduction to Smooth Manifolds John M. Lee

A Comprehensive Introduction to Differential Geometry Michael Spivak

First Steps in Differential Geometry Andrew Mclnerney


Introduction to Functional Analysis :

Introductory Functional Analysis with Applications Erwin Kreyszig

Principles of Functional Analysis Martin Schechter


Advanced Mathematical Analysis:

Real Analysis Elias M. Stein, Rami Shakarchi

Real and Complex Analysis Walter Rudin

Real Analysis Gerald B. Folland

Real Analysis H.L. Royden, P.M. Fitzpatrick


Introduction to Complex Analysis :

Complex Analysis John M. Howie

Complex Variables Mark J. Ablowitz

Visual Complex Analysis Tristan Needham

Complex Variables and Applications James Ward Brown, Ruel Churchill

Complex Analysis with Applications Dennis G. Zill


Introduction to Number Theory :

Elementary Number Theory David Burton

Elementary Number Theory with Applications Thomas Koshy

Elementary Number Theory Kenneth H. Rosen


Introduction to Abstract Algebra :

Contemporary Abstract Algebra Joseph A. Gallian

Algebra Michael Artin

Algebra Abstract and Concrete Frederick Goodman

A First Course in Abstract Algebra Joseph J. Rotman


Advanced Linear Algebra :

Linear Algebra Done Right Sheldon Axler

Linear Algebra Serge Lang

Finite-Dimensional Vector Spaces Paul R. Halmos

Linear Algebra Done Wrong Sergei Treil

Linear Algebra Georgi E. Shilov & Richard A. Silverman


Advanced Abstract Algebra :

Algebra Thomas Hungerford

Abstract Algebra David S. Dummit, Richard M. Foote

Advanced Modern Algebra Joseph J. Rotman

Algebra: A Graduate Course I. Martin Isaacs

Algebra Paul M. Cohn

A Course in Algebra  E.B. Vinberg

Algebra Serge Lang

Algebra: Chapter 0 Paolo Aluffi

Introduction to Commutative Algebra M. F. Atiyah & I. G. MacDonald


Algebraic Number Theory :

Number Fields Daniel A. Marcus

An Introduction to the Theory of Numbers Ivan Niven, Herbert S. Zuckerman, Hugh L. Montgomery


Motivation for Category Theory :

Conceptual Mathematics F. William Lawvere, Stephen H. Schanuel

Sets for Mathematics F.W. Lawvere, R. Rosebrugh

Arrows Structures and Functors: The Categorical Imperative Michael A. Arbib


Introduction to Category Theory :

Category Theory Steve Awodey

Category Theory in Context Emily Riehl

Basic Category Theory Tom Leinster

Abstract and Concrete Categories The Joy of Cats Jiri Adamek

Category Theory: A Gentle Introduction Peter Smith


Algebraic Topology Motivation :

Invitation to Combinatorial Topology Maurice Frechet and Ky Fan

Basic Concepts of Algebraic Topology Fred H. Croom

Basic Topology M.A. Armstrong

Topology John G. Hocking, Gail S. Young

Topology Klaus Janich


Introduction to Algebraic Topology :

Algebraic Topology: An Introduction William Massey

Algebraic Topology Allen Hatcher

A first course in Algebraic Topology C. Kosniowski

Elements of Algebraic Topology James Munkres


Algebraic Geometry Motivation :

Ideals Varieties and Algorithms David A. Cox, John Little, Donal O'Shea

Introduction to Algebraic Geometry Brendan Hassett


Introduction to Algebraic Geometry :

Basic Algebraic Geometry Igor R. Shafarevich

A Royal Road to Algebraic Geometry Audune Holme

Algebraic Geometry: A First Course Joe Harris

Elementary Algebraic Geometry Keith Kendig

Introduction to Algebraic Geometry Justin R. Smith


Euclidean and Non-Euclidean Geometry :

Foundations of Euclidean and Non-Euclidean Geometry Ellery B. Golos

Foundations of Geometry Gerard A. Venema

Euclidean and Non-Euclidean Geometry Marvin Jay Greenberg

The Four Pillars of Geometry John Stillwell

Modern Geometries John R. Smart

A Modern View of Geometry Leonard M. Blumenthal

Classical Geometry I. E. L., J. E. L., A. C. F. L., G. W. T.

Euclidean Geometry M. Solomonovich

Introduction To Non-Euclidean Geometry Harold E. Wolfe

Geometry D. A. Brannan, M. F. Esplen, J. J. Gray

Modern Geometry with Applications George A. Jennings

The Foundations of Geoemtry and the Non-Euclidean Plane George E. Martin

Projective Geometry H. S. M. Coxeter

Transformation Geometry George E. Martin