Astronomy Club

University of Arizona



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 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

Web Text

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 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

Common math errors

Approximation theory

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

Vector calculus

Numerical analysis

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  Advanced Math Books, Lectures, Videos Compilation

A-Level Maths Revision (UK) videos detailing exam solutions (also past papers from Edexcel)

Elementary Statistics

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

Tools & Apps

Wolfram Alpha All math homework threads should be looked up here before posting

SOCR Shitload of Statistics apps, games & tools

Triangle Solver

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 Examples

TeX Users Group

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.

Problems & Challenges

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)



Advice / Articles

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


Geometry Formulas & Facts

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