Advanced Mathematics Book List HIGHLY recommended Amazon book list with reviews. Assumes high-school level knowledge of math.
How to Become a Pure Mathematician (or Statistician) HIGHLY recommended a List of Undergraduate and Basic Graduate Textbooks and Lecture Notes – the blog
Precalculus: Mathematics for Calculus; James Stewart, Redlin, Watson
Calculus: Early Transcendentals; James Stewart
Calculus Made Easy Silvanus P. Thompson (1914) [Dated, but still very useful for gaining an intuitive grasp on certain concepts]
Principles of Mathematical Analysis; Walter Rudin [Real Analysis; colloquially called “Baby Rudin”]
Calculus: Graphical Numerical Algebraic; Ross L. Finney, Franklin Demana, Bert K. Waits, Daniel Kennedy
Mathematics (DOE-HDBK-1014-92) Vol I : Vol II [Department of Energy Fundamentals Handbooks]
Analytic Combinatorics A suggestion for further reading in an “Intro to Combinatorics” course
Free Math Books Math books
The Assayer Math Book Compilation
Amazon Mathematics Guide Undergraduate mathematics textbook recommendations
homepages.nyu.edu Advanced Math Books, Lectures, Videos Compilation
MathOnline Undergraduate to Research Level Books (Searchable)
17thCenturyMaths Bunch of famous historical translated maths books mainly from the 17th & 18th century
Mathematics Books
by Robert B. Ash, University of Illinois
Abstract Algebra: Theory and Applications by Thomas W. Judson, Stephen F. Austin State University
Advanced Calculus by Sternberg Shlomo and Lynn Loomis, Harvard University
Algebra 1 (Grades 9 & 10) by Andrew and Anne Gloag, High Tech High in San Diego, California
Algebra and Analysis for Computer Science by Jean Gallier, University of Pennsylvania.
Applied Probability by Paul Pfeiffer, Rice University
Basic Analysis by Jiří Lebl, University of Illinois at Urbana-Champaign
Basic Concepts of Mathematics by Elias Zakon, The University of Windsor
Basic Probability Theory by by Robert B. Ash, University of Illinois
Basic Probability and Statistics by Brenda Meery, high school mathematics teacher in Glace Bay, Nova Scotia
Book of Proof by Dr. Richard Hammack, Virginia Commonwealth University
Calculus (PDF) by David Guichard, Whitman College.
Calculus (PDF) by Gilbert Strang, MIT
Calculus 1 by Paul Dawkins, Lamar University
Calculus 2 by Paul Dawkins, Lamar University
Calculus 3 by Paul Dawkins, Lamar University
CK-12 Geometry (Grades 10-12) by multiple authors. Covers California curriculum.
CK-12 Single Variable Calculus (Grades 11-12) by Multiple authors. Covers California curriculum.
CK-12 Trigonometry – Second Edition (Grades 10-12) by multiple authors. Covers California curriculum.
Collaborative Statistics by Barbara Illowsky, Ph.D and Susan Dean, De Anza College
College Algebra by Paul Dawkins, Lamar University
Complex Analysis by George Cain, Georgia Institute of Technology
Complex Variables by Robert B. Ash, University of Illinois
A Computational Introduction to Number Theory and Algebra by Victor Shoup, NYU
A Course In Algebraic Number Theory by Robert B. Ash, University of Illinois
A Course In Commutative Algebra by Robert B. Ash, University of Illinois
Design of Comparative Experiments by R. A. Bailey, University of London
Difference Equations to Differential Equations: An Introduction to Calculus by Dan Sloughter, Furman University
Differential Equations by Paul Dawkins, Lamar University
Dynamical Systems by S. Sternberg, Harvard University
Electronic Statistics Textbook by T. Hill & P. Lewicki.
Elementary Abstract Algebra by W. Edwin Clark, University of Southern Florida
Elementary Calculus: An Infinitesimal Approach (PDF) by H. Jerome Keisler, University of Wisconsin-Madison
Elementary Linear Algebra by Keith Matthews, University of Queensland
Elementary Number Theory by W. Edwin Clark, University of Southern Florida
Elements of Abstract and Linear Algebra by Edwin H. Connell, University of Miami
First Course in Complex Analysis by Matthias Beck, Gerald Marchesi, and Dennis Pixton, SUNY – Binghamton
First Course in Linear Algebra by Dr. Robert Beezer, University of Puget Sound
GeneratingFunctionology by Herbert Wilf, University of Pennsylvania
Introduction to Matrix Algebra by Autar K Kaw, University of South Florida
Introduction to Probability (PDF) by Charles Grinstead & J. Laurie Snell, Swarthmore & Dartmouth Colleges
Introduction to Social Network Methods by Robert A. Hanneman and Mark Riddle, UC Riverside
Introduction to Statistical Thought by Michael Lavine, UMASS
Introduction to the Theory of Numbers by Leo Moser, McGill
Introductory Statistics: Concepts, Models, and Applications by David W. Stockburger, Missouri State
Lectures on Probability, Statistics and Econometrics by Marco Taboga, Economist, Bank of Italy
Lectures on Statistics by Robert B. Ash, University of Illinois
Linear Algebra (PDF) by Jim Hefferon, Saint Michael’s College
Linear Algebra by Paul Dawkins, Lamar University
Math Alive by Ingrid Daubechies, Princeton University
Math in Society by David Lipmann, Pierce College
Mathematical Methods of Engineering Analysis (PDF) by Erhan Çinlar and Robert J. Vanderbei, Princeton University
Multivariable Calculus by George Cain & James Herod, Georgia Tech
Proofs and Concepts: The Fundamentals of Abstract Mathematics by Dave Witte Morris and Joy Morris, University of Lethbridge
Real Variables with Basic Metric Space Topology by Robert B. Ash, University of Illinois
Statistics by Philip B. Stark, University of California – UC Berkeley
A Summary of Calculus by Karl Heinz Dovermann, University of Hawaii
The Book “A=B” by Marko Petkovsek, Herbert Wilf and Doron Zeilberger, Univ. of Pennsylvania and Rutgers
The Calculus of Functions of Several Variables by Dan Sloughter, Furman University
Yet Another Calculus Text by Dan Sloughter, Furman University
Online Math Course – free and comprehensive resource that is a collection of open college courses that spans videos, audio lectures, and notes
Betterexplained Some core math concepts explained intuitively
MathReference Primers on about every mathematical topic
Wikibooks/Mental Maths Mental Math
Purplemath Basic-Intermediate Algebra
Maths for Morons Like Us Basic – Intermediate Algebra
Virtual Math Lab Basic-Intermediate Algebra
Dave’s Short Trig Course Basic-Intermediate Trigonometry
Trig without Tears Basic-Intermediate Trigonometry (With emphasis on understanding)
Themathpage High School Math
S.O.S. Math Alegebra to Calculus
Harvey Mudd Math tutorials Precalculus through Linear Algebra
Paul’s Online Math Notes Math Notes
AoPS/Alcumus Learning system aimed at Gifted High Schoolers
Introduction to Logic Beginner’s Logic
Introduction to Group Theory Also goes into Rubix Cubes
MathPages Some advanced topics (Ancient website layout)
Analysis Webnotes Undergrad Math (Analysis)
MathOnline Undergraduate to Research Level Lecture Notes
MathCS.org Analysis
Book of Proof Intro to how to mathematically prove
Blogic Online Logic Textbook
Statsoft Statistics Online Book
The Little Handbook of Statistical Practice
SOCR Online Statistics Book
Numerical Analysis University of South Florida
Multivariable Calculus and Vector Analysis
Wolfram Math World Mathematics Encyclopedic
Cambridge Tripos example sheets
Basic Calculus ( Mathematics IA) – short ultimate basic calculus script
Linear equations (Mathematics IA)
Nonlinear equations (M IA)
Higher order equations (M IA)
Differential equations summary
WebMath Helpful links for hands-on math
Math Insight Includes narrative and interactive applets to teach topics in mathematics. Some topics include Multivariable Calculus and Vector Algebra
Khan Academy Arithmetic to Advanced (More emphasis on understanding)
PatrickJMT Arithmetic to Advanced (Less emphasis on understanding)
Brightstorm Algebra through Calculus
Youtube/derekowens Algebra to Calculus
Youtube/IntuitiveMath Algebra to Calculus
Youtube/njwildberger History, framework of mathematics & other topics
Midnight Tutors Calculus
The New Boston Math
Youtube/ MathTV Algebra through Calculus help
homepages.nyu.edu Advanced Math Books, Lectures, Videos Compilation
A-Level Maths Revision (UK) videos detailing exam solutions (also past papers from Edexcel)
Math In Real Life Organized collection of videos and webtext for high school mathematics
Meaure-Based Probability Series
Game Theory 101 Series describing introductory game theory
An Introduction to Number Theory By Edward Burger, 24 lectures
Calculus Lecture video series Does what it says on the tin!
Numerical Analysis Includes Euler’s Method, Trapezoidal Rule, Numerical Differentiation of Continuous Functions, and more.
Study Stove: Calculus Shows step by step how to do problems
Wolfram Alpha All math homework threads should be looked up here before posting
SOCR Shitload of Statistics apps, games & tools
Falstad Math Simulations/Applets
Multivariable calculus and vector analysis Readings on calc + Java simulations
PhET Math Java apps hosted by University of Colorado
Fractal Explorer With fractal explorer you can plot fractals and even make zoom videos from the mandelbrot set.
Getting to grips with LaTeX
Getting Started with LaTeX
MathURL Live LaTeX equation editing (can create links to each equation)
Detextify Draw characters in freehand to find its LaTeX character codes
TeXample.net Examples
MathIM Chat in LaTeX
AoPS/LaTeX LaTeX Reference
MathBin Pastebin with LaTeX
LaTeX video tutorials for complete beginners, quite nicely presented.
Minimal TikZ A minimal (and very understandable) introduction to plotting/graphs in LaTeX with the TikZ package.
Khan Academy/Exercises Basic – Intermediate Problem Generator (Click “Practice”)
nrich/Problem Generator Intermediate Math Problem Generator
Math Fun Facts Math paradoxes, theorems, puzzles, etc. explained such that a layman could understand
Senior Mathematical Challenge Papers ‘88 – ‘09 Questions (Aimed at 16-18)
Cut the Knot Math Puzzles & Problems
Mathschallenge Math Puzzles & Problems
nrich/Maths Math Puzzles & Problems
Wikipedia/ Unsolved Problems in Mathematics Good luck, son
British Mathematical Olympiad Download the papers separately or most of them in this pack (Pack contains all BMO1 & BMO2 up to 2011; no IMO papers)
Lockhart’s Lament Essay on the state of Math education
AoPS Math Advice
Mathematical Articles by Stan Brown
Terry Tao’s Blog / Advice Writing in Mathematics
Tim Gowers/ Advice About using examples in writing
Wikipedia/ Mathematical Maturity
Elements of Math by Steven Strogatz Series of articles on various topics in math
Xamuel Logic and Math blog
Tips for Calculus Tips on doing well in a calculus course
Wolfram MathWorld Wiki-like articles
ProofWiki
E-Calc Math Help Math reference & cheat sheets
MacTutor History of Mathematics
Earliest Uses of Mathematical Words
Earliest Uses of Mathematical Symbols
Tricki Store of Problem Solving techniques
Map of Mathematics Visualise the huge discipline of mathematics
The Online Encyclopedia of Integer Sequences
symbolab
desmos