Mathematic Readings

Algebra:
Algebra by I. Gelfand
Functions and graphs by I. Gelfand
The method of coordinates by I. Gelfand

Geometry:
Geometry: A High School Course by Serge Lang
Kiselev’s Geometry / Book I. Planimetry by A. P. Kiselev & Alexander Givental
Kiselev’s Geometry / Book II. Stereometry by A. P. Kiselev & Alexander Givental
Introduction to Geometry by H. S. M. Coxeter
Geometry Revisted by H.S.M. Coexter

Trigonometry:
Trigonometry by I.M. Gelfand

Pre-calculus:
Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by George F. Simmons

Calculus:
A First Course in Calculus by Serge Lang
Calculus and Analytic Geometry” by George Simmons

The Calculus Lifesaver: All the Tools You Need to Excel at Calculus by Adrian Banner
Calculus Made Easy by Silvanus P. Thompson

Calculus, Vol. 1 by Tom M. Apostol
Calculus by Michael Spivak
Calculus, Vol. 2 by Tom M. Apostol
Calculus On Manifolds by Michael Spivak

Problem Solving Books in Mathematic:
How to Think Like a Mathematician by Dr Kevin Houston
How to Prove It: A Structured Approach by Daniel J. Velleman
Problem-Solving Through Problems by Loren C Larson
How to Solve it by Polya
An Introduction to Mathematical Reasoning by Peter J Eccels
The Art and Craft of Problem Solving by Paul Zeitz
Problem-Solving Strategies (Problem Books in Mathematics) by Arthur Engel

Mathematical and Logic Puzzles:
The Lady or the Tiger?: and Other Logic Puzzles by Raymond M. Smullyan (age: 8 and up)
Entertaining Mathematical Puzzles by Martin Gardner (age: 10 and up)
My Best Mathematical and Logic Puzzles by Martin Gardner (age: 9 and 12)
Perplexing Puzzles and Tantalizing Teasers by Martin Gardner (age: 12 and up)
Alice in Puzzle-Land: A Carrollian Tale for Children Under Eighty by Raymond M. Smullyan (age: 80 and under)

Challenging Problems in Algebra by Alfred S. Posamentier (high school level)
Challenging Problems in Geometry by Alfred S. Posamentier (high school level)

Mathematical Puzzling by A. Gardiner (high school level)

Mathematical Puzzles: A Connoisseur’s Collection by Peter Winkler (high school, college, graduate level)
The Stanford Mathematics Problem Book: With Hints and Solutions by G. Polya (High school level)

Professor Povey’s Perplexing Problems: Pre-university Physics and Maths Puzzles with Solutions by Thomas Povey (College level)

Other masterpieces:
Alice in Wonderland by Lewis Carroll
Alice through the Looking Glass by Lewis Carroll
Alice Through the Needle’s Eye by Gilbert Adair
The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger (age: 10 and up)
Flatland by Edwin Abbott
A Mathematician’s Apology by G.H.Hardy
LockhartsLament by Paul Lockhart
The power of mathematics by Conway
Proofs from THE BOOK by Martin Aigner and Gunter Ziegler
Gödel, Escher and Bach: An Eternal Golden Braid by Douglas Hofstadter

Resources:
http://www.artofproblemsolving.com/store
http://math-blog.com/mathematics-books/
https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
http://www.springer.com/series/3423
http://www.springer.com/series/136
http://www.springer.com/series/714
http://store.doverpublications.com/by-subject-mathematics.html

Mathematic Readings

Mathematic Resources

How to study mathematics by Paul Dawkins
http://tutorial.math.lamar.edu/pdf/How_To_Study_Math.pdf
http://tutorial.math.lamar.edu/Extras/StudyMath/HowToStudyMath.aspx

Study skills in mathematics
http://www.maths.cam.ac.uk/undergrad/studyskills/text.pdf

Common math error by Paul Dawkins
http://tutorial.math.lamar.edu/pdf/Common_Math_Errors.pdf
http://tutorial.math.lamar.edu/Extras/CommonErrors/CommonMathErrors.aspx

“How to Read Mathematics” by Shai Simonson and Fernando Gouvea http://web.stonehill.edu/compsci//History_Math/math-read.htm

Advice to a Young Mathematician
http://press.princeton.edu/chapters/gowers/gowers_VIII_6.pdf

Stewart, I., “How to Learn Math,” Letters to a Young Mathematician, Basic Books, 2006, pp. 62-70. (AMS Book Review)
This letter is from a wonderful collection of letters from a mathematician to “Meg,” as she progresses from a high school student wondering whether higher levels of math are anything more than “bigger numbers and harder calculations,” to a tenured professor. The letters are unerringly encouraging while explaining myriad aspects of what it’s like to be a mathematician. The letter, “How to Learn Math,” is to Meg when she is a college student and explains what to do to get past sticking points when reading. The author also advises Meg to “read around the subject” to gain a sense of the larger picture within which any subject fits.
https://archive.org/download/LettersToAYoungMathematician/ian_stewartLettersToAYoungMathematician.pdf

Terry Tao’s https://terrytao.wordpress.com/advice-on-writing-papers/

Gerver, R., “Reading and Keeping a Research Journal,” Writing Math Research Papers: A Guide for Students and Instructors Key Curriculum Press, 2004.
This book chapter provides guidance for reading the literature relevant to a research project. Subsections include “Preparing to Read,” “Reading and Taking Notes,” and “Conquering Difficult Concepts.”

How to Develop a Mindset for Math by Kalid Azad:
http://betterexplained.com/articles/how-to-develop-a-mindset-for-math/

Habits of Mind:
http://www.withoutgeometry.com/2010/09/habits-of-mind.html

Collection of math notes
http://www.maths.cam.ac.uk/studentreps/res/notes.html

Paul Dawkins online math notes
http://tutorial.math.lamar.edu/

Paul Dawkins cheet sheets: http://tutorial.math.lamar.edu/cheat_table.aspx
Harold’s Cheat Sheets: http://www.toomey.org/tutor/harolds_cheat_sheets.html
and other cheat sheets at http://cheatsheets.org

Math guy handbook: http://www.mathguy.us/
Colecao Schaum’s (mathematical – formulas and tables)
http://florida.theorangegrove.org/og/file/3a8c652c-11d0-e967-95fb-b5bbae2586d6/1/math_handbook.pdf
Handbook for spoken mathematics Lawrence Cheng PhD

First steps in algebra by George Albert Wentworth
Beginning and intermediate algebra by Tyler wallance

Advanced high school mathematics by David b. Surowski
Fundament Concepts of Algebra
Trigonometric delights Eli Maor

PreCalculus by Carl Stitz and Jeff Zeager
PreCalculus an investigation of functions by David Lippman and Melonie Rasmussen
Funny Little Calculus Text by Robert Christ

How do undergraduates do mathematics? A guide to studying mathematics at Oxford University Charles Batty St. John’s College, Oxford
https://www0.maths.ox.ac.uk/system/files/study-guide/guide.pdf

Preparing for university calculus prepared by apics committee on mathematics and statistics edited by Robert Dawson
http://cs.smu.ca/apics/calculus/CalcPrep1.pdf

Advanced problems in core mathematics by Stephen siklos
http://www.maths.cam.ac.uk/undergrad/admissions/step/advpcm.pdf

Undergraduate Mathematics Reading List
http://www.maths.cam.ac.uk/undergrad/admissions/readinglist.pdf

Introduction to logic by Harry J. Gensler
Mathematical Reasoning writing and proof by Ted Sundstorm
Language proof and logic by Jon Barwise & John Etchemendy
Fundament Concepts of Mathematics
Book of proof by Richard Hammack

Websites:
https://reddit.com/r/math/comments/2mkmk0/a_compilation_of_useful_free_online_math_resources
http://khanacademy.org
http://artofproblemsolving.com
http://learner.org/courses/mathilluminated/
http://world.mathigon.org
http://betterexplained.com
http://www.artofmathematics.org
http://mathpuzzle.com
http://mathworld.wolfram.com
https://reddit.com/r/puremathematics
http://math.stackexchange.com
http://mathoverflow.net
http://mathinsight.org
http://proofwiki.org/wiki/Main_Page
http://encyclopediaofmath.org
https://oeis.org
http://arxiv.org
http://ams.org/notices
http://plus.maths.org

Mathematic Resources