So You Want to Study Mathematics… by Susan Rigetti (45 books)

A self study guide to mathematics, beginning at the undergraduate level, put together by Susan Rigetti. Please see her entire post on her website for details, commentaries, additional resources, and instructions on how to use this list. https://www.susanrigetti.com/math

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1	e: the Story of a Number by Eli Maor 3.94 avg rating — 2,169 ratings score: 100, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
2	The Joy of X: A Guided Tour of Math, from One to Infinity by Steven H. Strogatz (Goodreads Author) 4.05 avg rating — 8,762 ratings score: 99, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
3	Fermat's Enigma by Simon Singh 4.30 avg rating — 33,202 ratings score: 98, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
4	The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth by Paul Hoffman 4.06 avg rating — 10,005 ratings score: 97, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
5	The Man Who Knew Infinity: A Life of the Genius Ramanujan by Robert Kanigel (Goodreads Author) 4.03 avg rating — 8,876 ratings score: 96, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
6	Flatland: A Romance of Many Dimensions by Edwin A. Abbott 3.81 avg rating — 76,862 ratings score: 95, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
7	A Mathematician's Apology by G.H. Hardy 3.91 avg rating — 7,675 ratings score: 94, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
8	Fearless Symmetry: Exposing the Hidden Patterns of Numbers by Avner Ash 4.05 avg rating — 132 ratings score: 93, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
9	Proofs from the Book by Martin Aigner 4.40 avg rating — 862 ratings score: 92, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
10	Why Math? by R.D. Driver 3.67 avg rating — 9 ratings score: 91, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
11	Precalculus with Calculus Previews: . (The Jones & Bartlett Learning International Series in Mathematics) by Dennis G. Zill 4.14 avg rating — 7 ratings score: 90, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
12	Calculus: Early Transcendentals by James Stewart 3.97 avg rating — 971 ratings score: 89, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
13	Student Solutions Manual for Stewart's Single Variable Calculus: Early Transcendentals, 8th by James Stewart 3.88 avg rating — 17 ratings score: 88, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
14	Calculus Made Easy by Silvanus Phillips Thompson 4.23 avg rating — 1,252 ratings score: 87, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
15	Thomas' Calculus by Joel R. Hass 4.05 avg rating — 536 ratings score: 86, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
16	How to Prove It: A Structured Approach by Daniel J. Velleman 4.30 avg rating — 974 ratings score: 85, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
17	How to Solve It: A New Aspect of Mathematical Method by George Pólya 4.13 avg rating — 5,113 ratings score: 84, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
18	Introduction to Mathematical Thinking by Keith Devlin 3.94 avg rating — 542 ratings score: 83, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
19	Introduction to Linear Algebra by Gilbert Strang 4.24 avg rating — 694 ratings score: 82, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
20	Abstract Algebra by David S. Dummit 4.20 avg rating — 709 ratings score: 81, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
21	Understanding Analysis by Stephen Abbott 4.48 avg rating — 449 ratings score: 80, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
22	Principles of Mathematical Analysis by Walter Rudin 4.27 avg rating — 1,886 ratings score: 79, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
23	Real and Complex Analysis (Higher Mathematics Series) by Walter Rudin 4.29 avg rating — 461 ratings score: 78, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
24	Calculus by Michael Spivak 4.53 avg rating — 996 ratings score: 77, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
25	Combined Answer Book to Calculus, Third and Fourth Editions, spiral bound edition by Michael Spivak it was amazing 5.00 avg rating — 1 rating score: 76, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
26	Complex Analysis by Joseph Bak 3.60 avg rating — 30 ratings score: 75, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
27	Complex Analysis: . by Dennis G. Zill 3.69 avg rating — 13 ratings score: 74, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
28	Visual Complex Analysis by Tristan Needham 4.48 avg rating — 513 ratings score: 73, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
29	Ordinary Differential Equations (Dover Books on Mathematics) by Morris Tenenbaum 4.06 avg rating — 354 ratings score: 72, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
30	Differential Equations by Paul Blanchard 3.51 avg rating — 89 ratings score: 71, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
31	Student Solutions Manual for Blanchard/Devaney/Hall's Differential Equations, 4th by Paul Blanchard it was amazing 5.00 avg rating — 1 rating score: 70, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
32	Partial Differential Equations: An Introduction by Walter A. Strauss 3.64 avg rating — 88 ratings score: 69, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
33	Partial Differential Equations, Student Solutions Manual: An Introduction by Walter A. Strauss 3.58 avg rating — 19 ratings score: 68, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
34	Fourier Series (Dover Books on Mathematics) by Georgi P. Tolstov 4.17 avg rating — 116 ratings score: 67, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
35	Discrete Mathematics with Applications by Susanna S. Epp 4.02 avg rating — 405 ratings score: 66, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
36	A History of Mathematics by Carl B. Boyer 4.09 avg rating — 1,046 ratings score: 65, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
37	A Friendly Introduction to Number Theory by Joseph H. Silverman 4.30 avg rating — 86 ratings score: 64, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
38	An Introduction to the Theory of Numbers by G.H. Hardy 4.34 avg rating — 208 ratings score: 63, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
39	Thinking about Mathematics: The Philosophy of Mathematics by Stewart Shapiro 4.03 avg rating — 246 ratings score: 62, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
40	Philosophies of Mathematics by Alexander George 4.16 avg rating — 25 ratings score: 61, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
41	Philosophy of Mathematics: Selected Readings by Paul Benacerraf (Editor) 4.39 avg rating — 127 ratings score: 60, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
42	On Formally Undecidable Propositions of Principia Mathematica and Related Systems by Kurt Gödel 4.48 avg rating — 423 ratings score: 59, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
43	Gödel's Proof by Ernest Nagel 4.19 avg rating — 5,544 ratings score: 58, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
44	Experiments in Topology (Dover Books on Mathematics) by Stephen Barr 3.62 avg rating — 39 ratings score: 57, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars
45	Topology by James R. Munkres 4.30 avg rating — 1,227 ratings score: 56, and 1 person voted	Error rating book. Refresh and try again. Rate this book Clear rating 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars

45 books · 1 voter · list created October 8th, 2024 by Abbie (votes) .

Tags: abstract-algebra, algebra, calculus, complex-analysis, differential-equations, discrete-mathematics, guide, learn-math, learn-mathematics, learning-guide, linear-algebra, math, mathematician, mathematics, mathematics-textbooks, maths, modern-algebra, philosophy-of-mathematics, proofs, real-analysis, self-study, self-study-guide, study-math, study-mathematics, susan-fowler, susan-rigetti, textbooks, topology, university-level-mathematics

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message 1: by Abbie (last edited Oct 08, 2024 02:39PM) (new)

Oct 08, 2024 02:31PM

Please see the original post "So You Want to Study Mathematics…" on Susan Rigetti's website for full details, commentaries, and additional resources as well as full instructions on how to use this list for studying mathematics.

Below is the suggested order of study of the books in the list.

Before You Begin: Popular Math Books
e: The Story of a Number by Eli Maor (Level: Easy)
The Joy Of X: A Guided Tour of Math, from One to Infinity by Steven H. Strogatz (Level: Easy)
Fermat’s Enigma by Simon Singh (Level: Easy)
The Man Who Loved Only Numbers by Paul Hoffman (Level: Easy)
The Man Who Knew Infinity by Robert Kanigel
Flatland by Edwin A. Abbott (Level: Easy)
A Mathematician’s Apology by G.H. Hardy (Level: Medium)
Fearless Symmetry by Avner Ash and Robert Gross (Level: Difficult)
Proofs from THE BOOK by Martin Aigner and Günter M. Ziegler (Level: Difficult)

Prerequisites
Why Math? by R.D. Driver.
Precalculus with Calculus Previews by Dennis G. Zill and Jacqueline M. Dewar

Calculus
Calculus: Early Transcendentals, 8th Edition by James Stewart (essential); Student Solution Manual
Thomas' Calculus by Joel Hass, Christopher Heil, Maurice Weir (alternative)
Calculus Made Easy by Silvanus P. Thompson and Martin Gardner (supplement)

Introduction to Proofs
How to Prove It: A Structured Approach by Daniel J. Velleman (essential)
How to Solve It by G. Polya (supplement)
Introduction to Mathematical Thinking by Keith Devlin

Linear Algebra
Introduction to Linear Algebra, Fifth Edition by Gilbert Strang (essential)

Algebra
Abstract Algebra, 3rd Edition, by David S. Dummit and Richard M. Foote (up to chapter 9)

Real Analysis
Understanding Analysis, Second Edition, by Stephen Abbott (essential)
Principles of Mathematical Analysis, by Walter Rudin (essential)
Real and Complex Analysis by Walter Rudin (graduate level; optional)
Calculus by Michael Spivak; Answer Book

Complex Analysis
Complex Analysis, Third Edition, by Joseph Bak and Donald J. Newman (essential)
Complex Analysis: A First Course with Applications by Dennis G. Zill and Patrick D. Shanahan (essential)
Visual Complex Analysis, by Tristan Needham (supplement)

Ordinary Differential Equations
Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard (essential)
Differential Equations by Paul Blanchard, Robert L. Devaney, and Glen R. Hall (supplement); Student Solutions Manual.

Partial Differential Equations
Partial Differential Equations: An Introduction by Walter A. Strauss (essential); Student Solutions Manual
Fourier Series by Georgi P. Tolstov (essential)

Electives
Discrete Mathematics:
Discrete Mathematics with Applications by Susanna S. Epp

History of Mathematics:
A History of Mathematics by Carl B. Boyer and Uta C. Merzbach

Number Theory:
A Friendly Introduction to Number Theory by Joseph H. Silverman
An Introduction to the Theory of Numbers by G.H. Hardy and E.M. Wright

Philosophy of Mathematics:
Thinking about Mathematics: The Philosophy of Mathematics by Stewart Shapiro
Philosophies of Mathematics by Alexander George and Daniel J. Velleman
Philosophy of Mathematics: Selected Readings
On Formally Undecidable Propositions of Principia Mathematica (supplement)
Related Systems by Kurt Gödel (supplement)
Gödel's Proof by Ernest Nagel and James Newman (supplement)

Topology:
Experiments in Topology by Stephen Barr
Topology by James Munkres.

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