1 Reading List

1.1 Problem Solving

Introductory

Polya

Mathematics and Plausible Reasoning Vol 1 - Induction and Analogy in Mathematics. Polya
Mathematics and Plausibe Reasoning Vol 2 - Patterns of Plausible Inference. Polya
How to Solve It - A New Aspect of Mathematical Method. Polya
Mathematical Discovery - On Understanding, Learning, and Teaching Problem Solving. Polya

Teaching Math

Guide to Teaching Puzzle-based Learning. Meyer III, et al
How to Teach Mathematics (3rd ed). Krantz
Ahmes’ Legacy - Puzzles and the Mathematical Mind. Marcel Danesi
An Anthropology of PUzzles. Danesi

Higgins

Mathematics for the Curious. Higgins
Mathematics for the Imagination. Higgins
Nets, Puzzles, and Postmen - an Exploration of Mathematical Connections. Higgins

Problem-Solving and Mathematical Thinking

Ants, Bikes, and Clocks. William Briggs
Problem-solving Through Recreational Mathematics. Averbach, Chein
Discovering Mathematics - The Art of Investigation. Gardiner
A Mathematical Mosaic - Patterns & Problem-Solving. Ravi Vakil
Exploring Mathematics - Problem-solving and Proof. Grieser
Mathematical Thinking - Problem-Solving and Proofs (2nd ed). D’Angelo, West
Proofs and Refutations. Imre Lakatos
Wearing Gauss’s Jersey. Hathout
Mathematical Problem Solving. Schoenfield
How to Solve Problems. Wickelgren
Mathematical Problems - An Essay on Their Nature and Importance. Smorynski
Thinking Mathematically. Mason, Burton
Techniques of Problem Solving. Krantz
Essentials of Mathematical Thinking. Krantz
Mathematical Labyrinths - Pathfinding. Boris Pritsker
Expanding Mathematical Toolbox: Interweaving Topics, Problems, and Solutions. Boris Pritsker

Math-olympiad Oriented

The Art and Craft of Problem Solving. Zeitz
Problem-solving Through Problems. Larson
Mathematics as problem Solving (2nd ed). Soifer
Problem-solving Strategies. Engel
Winning Solutions. Lozansky, Rousseau
Principles of Mathematical Problem Solving. Erickson
Mathematical Olympiad Challenges (2nd ed). Andreescu, Gelca

Puzzle-books, and Problem Collections

Mathematical Puzzles - A Connoisseur’s Collection. Winkler
Wheels, Life, and Other Mathematical Amusements. Gardner
Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi. Gardner
Origami, Eleusis, and the Soma Cube. Gardner
Cows in the Maze and Other Mathematical Explorations. Stewart
The Magical Maze - Seeing the World Through Mathematical Eyes. Stewart
Math Hysteria - Fund and Games with Mathematics. Stewart
Mathematical Puzzling. Gardiner
Mathematical Mind Benders. Winkler
Sink or Float? - Thought Problems in Math and Physics. Kendig
Problems for Methematicians, Young and Old. Paul R. Halmos
Which Way Did the Bicycle Go - and Other Intriguing Mahtematical Mysteries. Konhauser, Velleman, Wagon
100 Great Problems of Elementary Mathematics - Their History and Solution. Doerrie
Professor Higgins’ Problem Collection. Higgins
Aha! Solutions. Martin Erickson
Mathematical Diamonds. Honsberger
Riddles in Mathematics. Northrop, Van Nostrand

Algorithmic Problem Solving and Computational Thinking

Algorithmic Problem Solving. Backhouse
Algorithmic Puzzles. Levitin, Levitin
Puzzles, Paradoxes, and Problem Solving - An Introduction to Mathematical Thinking. Reba, Shier
The Power of Computational Thinking - Games, magic and puzzles to help you become a computational thinker. Curzon, McOwan
Conjuring with Computation - A Manual of Magic and Computing for Beginners. Curzon, McOwan

Estimation, Soft Problem-solving Skills, Math in Everyday Life

Mathematics in Everyday Life. John Haigh
Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics. Robert B Banks
Guesstimation - Solving the World’s Problem on the Back of a Cocktail Napkin. Weinstein, Adam
Guesstimation 2.0 - Solving the World’s Problem on the Back of a Cocktail Napkin. Weinstein
Street-fithging Mathematics - The Art of Educated Guessing and Opportunistic Problem Solving. Mahajan
Strength in Numbers: Discovering the Joy and Power of Mathematics in Everyday Life. Sherman K Stein
The Invisible Power of Mathematics: The Pervasive Impact of Mathematical Engineering in Everyday Life. Samaey, Vandewalle
Conceptual Blockbusting - A Guide to Better Ideas. James L. Adams
Rapid Viz - A New Method for the Rapid Visualization of Ideas. Hanks, Belliston
Design it Yourself. Hansk, Belliston, Edwards
The Universal Traveler - A Soft-Systems Guide to Creativity, Problem-Solving, & the Process of Reaching Goals. Koberg, Bagnall
Experiences in Visual Thinking. McKim
Applied Imagination - Priciples and Procedures of Creative Thinking. Osborn
Wake Up Your Creative Genius. Hanks, Parry
Synectics - The Development of Creative Capacity. Gordon
The Metaphorical Way of Learning * Knowing - Applying Synectics to Sensitivity and Learning Situations. Gordon

General Math Books

Mathematics and Logic. Kac & Ulam
Mathematics -The Science of Patterns. Devlin
Mathematics - The Man Made Universe. Stein
Invitation to Mathematics. Konrad Jacobs
Uses of Infinity. Zippin
The Enjoyment of Mathematics - Selections from Mathematics for the Amateur. Rademacher, Toeplitz
Mathematics - From the Brith of Numbers. Jan Gullberg
Mathematics for the Million. Hogben
The Pleasures of Counting. Koerner
The Search for Pattern. Sawyer
Mathematicians Delight. Sawyer
A Path to Modern Mathematics. Sawyer
Concepts of Modern Mathematics. Ian Stewart
Mathematical Vistas - From a Room With Many Windows. Hilton, Holton, Pedersen
A Mathmeatical Tapestry - Demonstrating the Beautiful Unity of Mathematics. Hilton, Pedersen
The Role of Mathematics in Science. Schiffer, Bowden
Mathematical Methods in Science. Polya
Ingenuity in Mathematics. Honsberger
A Mathematicians Lament - How School Cheats Us Out of Our Most Fascinating and Imaginative Art. Paul Lockhart
Arithmetic. Paul Lockhart
Measurement. Paul Lockhart
The Art of the Infinite - The Pleasures of Mathematics. Kaplan, Kaplan
Astronomer Priest and Ancient Mariner. Hogben
Mathematics - From the Brith of Numbers. Gullberg
Alice in Wonderland - A Student’s Guide to the Enjoyment of Higher Mathematics. Baylis, Haggarty
The Concept of Number: From Quaternions to Monads and Topological Fields. Artmann

Proofs

The Book of Proof. Hammack
Proofs - A Long-Form Mathematics Textbook. Cummings
Reading, Writing, and Proving - A Closer Look at Mathematics. Daepp, Gorkin
Charming Proofs - A journey Into Elegant Mathematics. Alsina, Nelsen
Mathematical Proofs - A Transition to Advanced Mathematics. Chartrand, Polimeni, Zhang
How to Prove it - A Structured Approach. Velleman

Practical Mathematical Models (Physical Objects)

Mathematical Models. Cundy
Designing and Making. Sawyer

1.2 Symmetry

General, Intro

Symmetry Rules - How Science and Nature Are Founded on Symmetry. Joe Rosen
Symmetry, Shape, and Space - An Introduction to Mathematics Through Geometry. Kinsey, Moore
Symmetry - Cultural-historical and Ontological Aspects of Science-Arts Relations, The Natural and Man-Made World in an Interdisciplinary Approach. Darvas
Manifold Mirrors - The Crossing Paths of the Arts and Mathematics. Felipe Cucker
Symmetry - A Journey Into the Patterns of Nature. Sautoy
Symmetry. Walser
Symmetry Discovered. Rosen
The Equation That Couldn’t Be Solved - How Mathematical Genius Discovered the Language of Symmetry. Mario Livio
Connections - The Geometric Bridge Between Art and Science. Jay Kappraff
Symmetry and the Monster - One of the greateset Quests of Mathematics. Ronan
Fearful Symmetry - is God a Geometer? Ian Stewart, Martin Golubitsky
Symmetry - Unifying Human Understanding. Hargittai
Beyond Measure - A Guided Tour Through Nature, Myth, and Number. Jay Kappraff
Symmetry - A Unifying Concept. Hargittai, Hargittai
Symmetry and the Beautiful Universe. Lederman

Golden Ration Specific

The Divine Proportion - A Study in Mathematical Beauty. Huntley
Der Goldene Schnitt. Beutelspacher, Petri
The Golden Ratio - The Story of Phi, The World’s Most Astonishing Number. Mario Livio
the Golden Ratio - The Divine Beauty of Mathematics. Gary B. Meisner
The Golden Section. Hans Walser

Physical, Chaos, Fractals

Chaos and Fractals - New Frontiers of Science (2nd ed). Peitgen, Juergens, Saupe
Fractals, Chaos, Power Laws - Minutes from an Infinite Paradise
Symmetry and Complexity - The Spirit and Beauty of Nonlinear Science. Mainzer
The Comprehensible Cosmos - Where do the Laws of Physics Come From? Stenger
Lawas and Meta-laws of nature: Conversation Laws and Symmetries. Marc Lange
Similarities in Physics. Shive, Weber
Perpetual Motion - Electrons and Atoms in Crystals. Alec T Stewart
Symmetry in Chaos - A Search for Pattern in Mathematics, Art, and Nature (2nd ed). Field, Golubitsky
Complexity - A Guided Tour. Melanie Mitchell
Symmetries in Physics - Philosophical Reflections. ed Brading, Castellani
Classification, Symmetry, and the Periodic Table. William B Jensen
Asymmetry: The Foundation of Information. Scott J. Muller
The Fabric of the Cosmos - Space, Time, and the Texture or Reality. Brian Greene
The Ghost in the Atom. ed Davies, Brown
Information and Its Role in Nature. Roederer

Fractals Specific

Fractals - A Very Short Introduction. Falconer
Chaos and Fractals - An Elementary Introduction. Feldman
The Fractal Geometry of Nature. Mandelbrot
Fractals and Chaos - An Illustrated Course. Addison
Fractals for the Classroom Part One - Introduction to Fractals and Chaos. Peitgen, Juergens, Saupe
Introduction to Fractals and Chaos. Crownover
Chaos, Bifurcations, and Fractals Around Us - A Brief Introduction. Szepmlinka-Stupnicka
Chaotic Dynamics - An Introduction Based on Classical Mechanics. Tel, Gruiz
Chaotic Dynamics - Fractals, Tilings, and Substitutions. Goodson
Measure, Topology, and Fractal Geometry. Edgar
Fractal Geometry - Mathematical Foundations and Applications. Falconer
Exploring Randomness. Chaitin

Group Theory, Algebra, Mathematical

Symmetries. Johnson
Algebra - Abstract and Concrete. Goodman
Differential Equations - Their Solution Using Symmetries. Stephani, Maccallum
Equivalence, Invariants, and Symmetry. Olver

Visual, Design, Solid Geometry

Logic and Design - In Art, Science, and Mathematics. Krome Barrat
Fragments of Inifnity - Kaleidoscope of Math and ARt. Ivars Peterson
Visual Symmetry. Hargittai, Hargittai
Geometry of Design - Studies in Proportion and Composition. Kimberly Elam
The Geometry of Art and Life. Matila Ghyka
A Practical Handbook of Geometrical Composition and Design. Matila Ghyka
The Elements of Dynamic Symmetry. Jay Hambridge
The Beautiful Necessity - Seven Essays on Theosophy and Architecture. Claude Bragdon
The Geometrical Foundation of Natural Structure - A Source Book of Design. Robert Williams
Order in Space - A Design Source Book. Keith Critchlow

Analogy

Models and Analogies in Science. Mary Hesse
Surfaces and Essences - Analogy as the Fuel and Fire of Thinking. Douglas Hofstadter, Emmanuel Sander
The Metaphorical Way of Learning & Knowing - Applying Synectics to Sensitivity and Learning Situations. Gordon, Poze

Alternative

The Myth of Invariance - The Origin of the Gods, Mathemateics and Music From the Rg Veda to Plato. Ernest G McClain
Philomath - The Geometric Unification of Science and Art Through Number. Grant, Ghannam
Quadrivium - The Four Classical Liberal Arts of Number, Geometry, Music & Cosmology. Keith Critchlow
Mathematics Useful for Understanding Plato. Theon of Smyrna

1.3 Geometry

Constructive Geometry

Drawing Geometry. John Allen
Ruler & Compass - Practical Geometric Constructions. Andrew Sutton
Exploring Classical Greek Construction Problems with Interactive Geometry Software. Meskens, Tytgat
Construction of Polygons. Duerer
Geometric Constructions. Martin

Design & Compositoin

Geometrical Composition and Design. Ghyka
Geometry of Design - Studies in Proportion and Composition. Elam

Engineering Graphics

Geometric and Engineering Drawing (4th ed). Kenneth Morling

Classical Foundations

Geometry - A Highschool Course. Lang, Murrow
Geometry (2nd ed). Harold R Jacobs
Geometry Revisited. Coxeter, Greitzer
Geometry. Gelfand

Broad Classical & Early Modern Overview

Classical Geometry - Euclidean, Transformational, Inversive, and Projective. Leonard, Lewis, Liu, Tokarsky
Geometry: Euclid and Beyond. Robin Harsthorne
Geometry (2nd ed). Brannan, Esplen, Gray
The Four Pillars of Geometry. Stillwell
Continious Symmetry - from Euclid to Klein. Banker, Howe
Plane and Solid Geometry. Aarts
The Geometric Viewpoint - A Survey of Geometries. Sibley
Geometry - Plane and Fancy. Singer
A Survey of Geometry (2nd ed). Eves
The Foundations of Geometrey and the Non-Euclidean Plane. Martin
Geometry - A Comprehensive Course. Dan Pedoe
Geometry and The Imagination. Hilbert, Cohn-Vossen

Tranformational & Projective Geometry

Geometric Transfomrations I, II, III. Yaglom
Transformational Plane Geometry. Umble, Han
Projective Geometry: From Foudnations to Applications. Beutelspacher, Rosenbaum
Geometrische Perspektive. Rehbock

Surfaces, Differential Geometry & Modern Bridges

The Shape of Space (3rd ed). Weeks
The Geometry of Curves. Rutter
Geometry of Surfaces. Stillwell
Geometry. Audin
Euler’s Gem - The Polyherdron Formula and the Brith of Topology. Richeson
Geometry and Topology. Reid, Szendroi

Conceptual Supplements & Other Topics

Conics and Cubics - A Concrete Introduction to Algebraic Curves. Robert Bix
Complex Numbers and Geometry. Hahn
Journey into Geometries. Coxeter, Stillwell

1.4 Discrete Mathematics

General

Mathematical Structures for Computer Science - Discrete Mathematics and Its Applications. Gersting
Discrete Mathematics for Computer Science. Golovnev
Diskrete Mathematik fuer Einsteiger - Mit Anwendungen in Technik und Informatik. Beutelspacher, Zchiegner
Discrete Mathematics for Computer Science - An Example-Based Introduction. Jon Pierre Fortney
Introduction to Mathematical Structures and Proof. Gerstein
Discrete Mathematics. Chartrand, Zhang
Discrete Mathematics and its Applications. Rosen
Discrete and Combinatorial Mathematics. Grimaldi
Discrete Mathematics. Johnsonbauch
Discrete Mathemetics for Computer Science. David Liben-Nowell
Discrete Mathematics and Functional Programming. VanDrunen
Concrete Mathematics. Knuth, Graham

Combinatorics

Older Intro

Mathematics of Choice or How to Count Without Counting. Ivan Niven
Introduction to Combinatorics (1972). Berman, Fryer
Principles of Combinatorics (1971). Berge

General Intro

Introductory Combinatorics. Brualdi
Combinatorics Through Guided Discovery. Bogart
Applied Combinatorics (3rd ed). Roberts, Tesman
Introduction to Combinatorics. Martin J Erickson
Counting - the Art of Enumerative Combinatorics. George E Martin
How to Count - An Introduction to Combinatorics and Its Applications. Beeler
A Walk Through Combinatorics - An Introductin to Enumeration and Graph Theory. Miklos Bona
Applied Combinatorics. Alan Tucker

Advanced

Combinatorial Mathematics (has solution manual). Douglas B West
Aspects of Combinatorics - A wide-randing Introduction. Victor Bryant
Combinatorics - Topics, Techniques, Algorithms. Peter Cameron

Math Olympiad & Problem Oriented

Applied Combinatorics with Problem Solving. Jackson, Thoro
Combinatorics - A Problem Oriented Approach. Daniel A Marcus
Principles and Techniques of Combinatorics. (has solution manual) Chuan-Chong, Khee-Meng
Problem-Solving Methods in Combinatorics - An Approach to Olympiad Problems. Pablo Soberon
Combinatorics - A Problem-based Approach. Mladenovic
A Path to Combinatorics for Undergraduates - Counting Strategoes. Andreescu, Feng
Combinatorics. Vilenkin
Geometric Etudes in Combinatorial Mathematics. Soifer

Graph Theory

General, Intro

Graphs and Their Uses. Ore
Graph Theory - A Problem-oriented Approach. Daniel A Marcus
Graphen fuer Einsteiger. Nitzche
A First Course in Graph Theory. Chartrand, Zheng
Graph Theory - an Introduction to Proofs, Algorithms, and Applications. Saoub
A First Look at Graph Theory. Clark, Holton
Introduction to Graph Theory (2nd ed). (has sol manual). Douglas West
Graph Theory with Applications. Bondy

Algorithmic

Algorithmic Graph Theory. Gibbons
Algorithmic Graph Theory. McHugh

Conceptual, Supplementary

The Fascinating World of Graph theory. Chartrand, Zhang
Nets, PUzzles, and Postmen - an Exploration of Mathematical Connections. Peter M Higgins

Number Theory

Number Theory - A Historical Approach. John J Watkins
Elementary Number Theory & its Applications (6th ed). Rosen
Elementary Number theory. Jones, Jones
Elementary Number Theory in Nine Chapters (2nd ed). Tattersall
Recreations in the Theory of Numbers. Albert H Beiler
A Friendly Introduction to Number Theory. Silverman
A Guide to Elementary Number Theory. Dudley

Computational, Programming

Elementary Number Theory: Primes, Congruences, and Secrets - A Computational Approach with Sagemath. Stein
Number Theory in Context and Interactive. Karl-Dieter Crisman
Primes and Programming - An Introduction to Number Theory with Computing. Peter Giblin

Conceptual, Supplementary

From Zero to Infinity - What makes Numbers Interesting. Constance Reid
Das Kleine Buch der Zahlen - Vom Abzaehlen bis zur Kryptographie. Peter M Higgins
The Book of Numbers. Conway, Guy

Crytpography / Crytpology

Introduction to Cryptography with Open Source Software. Alasdair McAndrew
Understanding Cryptography - A Textbook for Students and Practitioners. Paar, Pelzl
Cryptology. Albert Beutelspacher

Cryptanalysis

Decrypted Secrets - Methods and Maxims of Cryptology. Bauer
Elementary Cryptanalysis. Sinkov
Cryptanalysis - A Study of Ciphers and their Solution. Helen Fouche Gaines

Applied Cryptography / Cybersecurity

Implementing Cryptography Using Python. Shannon W Bray
Full Stack Python Security - Cryptography, TLS, and attack Resistance. Dennis Byrne
Cracking Codes with Python - An Introduction to Building and Braking Ciphers. Sweigart

Coding Theory

Introduction to Cryptography with Coding Theory (2nd ed). Trappe, Washington
Codes - An Introduction to Information, Communication, and Cryptography. Norman L Biggs

Mathmematical Logic

General

Proof and Disproof in Formal Logic - An Introduction for Programmers. Richard Bornat
Logic and Structure. Dirk van Dalen
Logical Labyrinths. Smullyan
Mathematical Logic. Joseph Mileti
Computability and Logic (5th ed). Boolos, Burgess, Jeffrey
The Mathematics of Logic - a Guide to Completeness Theorems and Their Applications. Richard Kaye

Computational

Modelling Puzzles in First Order Logic. Adrian Groza
Logic for Applications. Nerode
The Computer Modelling of Mathematical Reasoning. Bundy

Intuitionistic

On the Meanings of the Logical Constants and the Justifications of the Logical Laws. Per Martin-Loef

Set Theory

Set Theory for Computer Science. Glynn Winskel
Logic, Induction and Sets. Thomas Forster
Set Theory. Derek Goldrei

1.5 Abstract Algebra

Intro

Concrete Approach to Abstract Algebra. Sawyer
Concrete Algebra - With a View Toward Abstract Algebra. McKay
Sets, Groups, and Mappings - An Introduction to Abstract Mathematics. Hwang
Algebra and Geometry. Beardon
Integers, Polynomials, and Rings. Irving

Core

Contemporary Abstract Algebra. Gallian
Abstract Algebra - An Interactive Approach. William Paulsen
Abstract Algebra - An Inquiry-based Approach. Hodge, Schlicker, Sunstrom
Abstract Algebra - Structures and Applications. Stephen Lovett
Abstract Algebra - A First Course. Stephen Lovett
Introduction to Abstract Algebra. Jonathan D R Smith
Abstract Algebra - A Gentle Introduction. Mullen, Sellers

With Applications

Abstract Algebra with Applications. Terras
Concrete Abstract Algebra. From Numbers to Groebner Bases
Introduction to Applied Algebraic Systems. Reilly

Next Steps, Alternative

Abstract Algebra - An Introduction. Hungerford
Algebra - Notes From the Underground. Aluffi
Algebra: Chapter 0. Aluffi
Visual Group Theory. Nathan Carter
Universal Algebra. Burris, Sankappanavar

1.6 Lienar Algebra

Basic, Intro

An Engineering Approach to Linear Algebra. W W Sawyer
Linear Aglebra (4th ed). Jim Hefferon
Linear Algebra and Geometry. Cuoco et al
Linear Algebra and Its Applications. Lay, Lay, McDonald
Linear Aglebra Done Right. Sheldon Axler.
Introduction to Linear Algebra. Strang
Introduction to Linear and Matrix Algebra. Nathaniel Johnston
Linear Algebra. Meckes, Meckes
Linear Algebra - A Modern Introduction (4th ed). Poole
Linear Algebra with Applications. Otto Bretscher
A Modern Introduction to Linear Algebra. Henry Ricardo
Linear Algebra - Geometry and Transformation. Bruce Solomon
Practical Linear Algebra - A Geometry Toolbox (4th ed). Farin, Hansford
Linear Algebra - Concepts and Applications. Bogacki

Linear Algebra with CAS

Linear Algebra - Theory, Intuition, Code (python & matlab). Cohen
Linear Algebra and its Applications with R. Yoshida

With Applications

Applied Linear Algebra and Matrix Analysis. Thomas S Shores
Introduction to Applied Linear Algebra - Vectors, Matrices, and Least Squares. Boyd, Vandenberghe
Matrix Analysis and Applied Linear Algebra. Meyer
Applied Linear Algebra. Olver, Shakiban
Matrix Methods - Applied Linear Algebra and Sabermetrics (4th ed). Bronson, Costa
Linear Algebra and its Applications. Peter Lax
Linear Algebra and Learning from Data. Gibert Strang
Linear Algebra and Matrix Analysis for Statistics. Benerjee, Roy

Second Course, Advanced

Advanced Linear and Matrix Algebra. Nathaniel Johnston
A Second Course in Linear Algebra. Garcia, Horn

Numerical LA

Numerical Linear Algebra - An Introduction. Wendland
Applied Numerical Linear Algebra. Hager

1.7 Analysis

Intro, First Steps

Numbers and Functions (2nd ed). Burn
Limits, Limits Everywhere. Applebaum
Numbers, Sequences, and Series. Hirst
Guide to Analysis. Mary F Hart
Infinite Processes - Background to Analysis. Gardiner
Calculus by and for Young People. Don Cohen

Core Track

Analysis. P E Kopp
Elementary Analysis - The Theory of Calculus. Ross
A First Course in Mathematical Analysis. Brannan
Mathematical Analysis - A Straightforward Approach. Binmore
Introduction to Real Analysis. Bartle, Sherbert
Real Mathematical Analysis. Pugh
A First Course in Analysis. Pedrick
Mathematical Analysis - An Introduction. Browder
includes: topology, function spaces, diffable maps, measures, integration, manifolds, multilinear algebra etc

Later: Books by Lackzovich, and Zorich (Russia)

Advanced

Measure, Integral and Probability. E Kopp

With Applications

Real Analysis and Applications. Davidson, Donsig

1.8 General Applied Math

Advanced Engineering Mathematics. Dennis G Zill
Advanced Engineering Mathematics. Kreyszig
Advanced Engineering Mathematics. Greenberg
Introduction to Applied Mathematics. Sirovich
Mathematical Methods in the Physical Sciences. Mary L Boas

Mathematical Methods for Physicists

Mathematical Methods for Physicists (5th ed). Arfken, Weber
The Road to Reality. Penrose

Mathematical Modelling

Modeling and Simulation in Python. Allen B Downey
A Programmer’s Introduction to Mathematics. Jeremy Kun
Introduction to the Foundations of Applied Mathematics. Holmes
An Invitation to Applied Mathematics - Differential Equations, Modeling, and Computation. Chicone

Fourier Analysis

Fourier Analysis with Applications. Filtering, Numerical Computation, Waveletts. Gasquet, Witomski

1.9 Topology and Metric Spaces

Topology

Elements of Abstract Analysis & Set Theory

Real Analysis with Point-Set Topology
The Foudnations of Analysis: A Straightforward Introduction - Book 2 Topological Ideas. Binmore
Elements of Abstract Analysis. Searcoid
Classic Set Theory. Goldrei

Intro

Topological Spaces. Buskes, Rooij
First Concepts of Topology. Chinn, Steenrod
A Guide to Topology. Krantz
Introduction to Topology. Mendelson
A Topological Aperitif. Huggett, Jordan

Core Track

Introduction to Metric & Topological Spaces. Sutherland
Topology Through Inquiry. Starbird, Su
Basic Topology. Armstrong
Essential Topology. Martin D Crossley
Topology (2nd ed). Munkres

Metric Spaces

Metric Spaces. Michael O Searcoid
Metric Spaces - Iteration and Application. Victor Bryant

Visual, Intuitive, Alternative

Shape of Space (3rd ed). Jeffrey R Weeks
Flatland. Edwin Abott
Intuitive Topology. Prasolov
Experiments in Topology. Stephen Barr

1.10 Single and Multivariable Calculus

Single Variable Calculus

A First Course in Calculus. Lang
Calculus. Spivak
Calculus in Context. Callahan, Hoffman
Calculus with Applications. Lax, Shea

long running:

calculus. Stewart, clegg, watson

Multivariable Calculus

Intro

Calculus of Several Variables. Serge Lang
Functions of Two Variables. Sean Dineen

Core Track

Vector Calculus (6th ed). Marsen, Tromba
Vector Calculus, Linear Algebra, and Differential Forms - A Unified Approach (5th ed). Hubbard, Hubbard
Vector Calculus. Matthews
Advanced Calculus - A Geometric View. Callahan
An Illustrative Guide to Multivariable and Vector Calculus. Miklavcic
Multivariable Calculus with Applications. Lax, Terrell
Multivariate Calculus and Geometry (3rd ed). Sean Dineen
Calculus and Analysis in the Euclideane Space. Jerry Shurman
A Course in Multivariable Calculus and Analysis. Ghorpade, Limaye

Mutidomensional Real Analysis

Multidimensional Real Analysis I - Differentiation. Duistermaat, Kolk
Multidimensional Real Analysis II - Integration. Duistermaat, Kolk

With CAS

Multivariable Calculus with MATLAB - With Applications to Geometry and Physics. Lipsman, Rosenberg
Multivariable Calculus with Mathematica. Shoushani, Gilbert

Advanced Calculus, Math for Physicists

Advanced Calculus. Kaplan
Advanced Calculus. R Creighton Buck
Mathematical Methods for Physics and Engineering. Riley, Hobson, Bence
Advanced Calculus. Sternberg

1.11 Funcional and Complex Analysis

Complex Analysis

A First Course in Complex Analysis with Applications. Zill, Shanahan
Complex Analysis. Howie
Visual Complex Analysis. Needham
Complex Analysis. Gamelin
Complex Analysis. Donald Marshall
Complex Analysis - A Visual and Interactive Introduction. Juan Carlos Ponce Campuzano

Functional Analysis

Functional Analysis - An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras. Joseph Muscat
Linear Functional Analysis. Youngson
Metrics, Norms, Inner Products, and Operator Theory. Christopher Heil
Introductory Functional Analysis with Applications. Kreyszig
Theoretical Numerical Analysis - A Functional Analysis Framework (3rd ed). Atkinson, Han
Introductory Functional Analysis - With Applications to Boundary Value Problems and Finite Elements. Daya Reddy

1.12 Differential Equations

Intro

An Introduction to Ordinary Differential Equations. James C Robinson
Differential Equations (4th ed). Blanchard, Devaney, Hall
A First Course in Differential Equations - with Modelling Applications. Zill
Introduction to Differential Equations (3rd ed). Holmes
Differential Equatins and Linear Algebra (4th ed). Edwards, Penney
Differential Equations and Linear Algebra. Gilbert Strang
Differential Equations and Their Applications. Braun
Ordinary Differential Equations. Adkins, Davidsog
Ordinary Differential Equations - Applications, Models, and Computing. Charles E Robers Jr

Theory & Qualitative

Differential Equations, Dynamical Systems, and an Introduction to Chaos. Hirsch, Smale
The Theory of Differential Equations - Classical and Qualitative. Kelley, Peterson
Ordinary Differential Equations. Vladimir I Arnold
Ordinary Differential Equations with Applications. Chicone
Differential Equations and Dynamical Systems (3rd ed). Lawrence Perko

PDE

Partial Differential Equations for Scientists and Engineers. Farlow
Introduction to Partial Differential Equations. Peter J Olver
Applied Partial Differential Equations (3rd ed). David Logan
Partial Differential Equations - Analytical Methods and Applications. Henner, Belozerova, Nepomnyaschy

1.13 Dynamical Systems

Intro

From Calculus to Chaos. D J Acheson
Introduction to Dynamic Systems - Theory, Models, and Applications. David G Luenberger

Core Track

Differential Equations, Dynamical Systems, and an Introduction to Chaos (3rd ed). Hirsch, Smale, Devaney
Chaos - An Introduction to Dynamical Systems. Alligood, Sauer, Yorke
Dynamical Systems - Differential Equations, maps, and Chaotic Behvaiour. Arrowsmith
Dynamical Systems with Applications using MATLAB. Stephen Lynch
Differential Dynamical Systems. James D Meiss

Visual

Dynamics - The Geometry of Behavior (2nd ed). Abraham, Shaw

Advanced

Introduction to the Modern Theory of Dynamical Systems. Katok, Hasselblatt

Nonlinear Dynamics & Chaos

The Essence of Chaos. Lorenzelli
Chaos and Nonlinear Dynamics - An Introduction for Scientists and Engineers (2nd ed). Robert C Hilborn
Nonlinear Dynamics and Chaos - With Applications to Physics, Biology, Chemistry, and Engineering. Strogatz
Chaos in Dynamical Systems. Ott
Introduction to Applied Nonlinear Dynamical Systems and Chaos (2nd ed). Stephen Wiggins
Synchronization - A Universal Concept in Nonlinear Science. Pikovsky, Rosenbaum

Discrete Dynamical Systems

Introdution to Mathematical Modeling Using Discrete Dynamical Systems. Frederick R Morotto
Introduction to Discrete Dynamical Systems and Chaos. Martelli
A First Course in Discrete Dynamical Systems. Holmgren
Discrete Dynamical Systems. Galor
An Introduction to Difference Equations. Elaydi

Analytical Mechanics

Introduction to Modern Dynamics. Nolte
Mechanics. From Newton’s Laws to Deterministic Chaos. Florian Scheck
Physics for Mathematicians - Mechanics I. Spivak
Advanced Dynamics. Donald T Greenwood
Analaytical Mechanics. Fasano, Marmi
Analytical Mechanics. Hand, Finch
Classical Dynamics - A Contemporary Approach. Jose, Saletan
Essentials of Hamiltonian Dynamics. Lowenstein
Lectures on Classical Mechanics. John C Baez
Mathematical Methods of Classical Mechanics (2nd ed). V I Arnold
Foundations of Mechanics. Abraham, Marsden
Geometric Mechanics on Riemannian Manifolds - Applications to Partial Differential Equations. Ovidiu Calin, Der-Chen Chang
Geometric Mechanics - Toward a Unification of Classical Physics. Talman
Geometric mechanics and Summetry - From finite to Infinite Dimensions. Darryl Holm, Cristina Stoica
Advanced Analytical Dynamics. De Sapio

1.14 Differential Geometry & Manifolds, Lie Algebras

Diffgeo Intro

Diffgeo of Curves and Surfaces

Differential Geometry of Curves and Surfaces. do Carmo
Differential Geometry of Curves and Surfaces (2nd ed). Banchoff, Lovett
Elementary Differential Geometry. Andrew Pressley
Differential Geometry - Curves, Surfaces, Manifolds (2nd ed). Wolfgang Kuehnel

Intro

Visual Differential Geometry and Forms - A Mathematical Drama in Five Acts. Needham
Geometry from a Differentiable Viewpoint (2nd ed). John McCleary
Manifolds, Vector Fields, and Differential Forms - An Introduction to Differential Geometry. Gross, Meinrenken
First Steps in Differential Geometry - Riemannian, Contact, Symplectic. Andrew McInerney
Introduction to Differential Geometry. Robbin, Salomon
A Visual Introduction to Differential Froms and Calculus on Manifolds. Jon Pierre Fortney

Diffgeo of Physics

Modern Differential Geometry for Physicists (2nd ed). Chris J Isham
Applied Differential Geometry. William L Burke
Differential Geometry and Lie Groups for Physicists. Fecko
Topology, Geometry, and Gauge Fields - Foundations (2nd ed). Gregory L Naber
The Geometry of Physics - An Introduction. Theodore Frankel
Riemannian Geometry
Riemannian Geometry. do Carmo
Riemannian Geometry (3rd ed). Gallot, Hulin, Lafontaine

Manifolds

An Introduction to Multivariable Analysis - from Vector to Manifold. Mikusinski, Taylor
An Introdution to Manifolds. Spivak
An Introduction to Manifolds. Lowing W Tu
Differentiable Manifolds (2nd ed). Lawrence Conlon
An Introduction to Differential Manifolds. Jacques Lafontaine

Advanced

Introduction to Smooth Manifolds (2nd ed). John M Lee
Introduction to Topological Manifolds. John M Lee
Analysis on Manifolds. Munkres

Lie Algebras

Naive Lie Theory. Stillwell
Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics. Sattinger, Weaver
Foundations of Differentialbe Manifolds and Lie Groups. Frank W Warner
Lie Groups, Physics, and Geometry - An Introduction to Physicists, Engineers and Chemists. Robert Gilmore
Lie Groups, Lie Algebras, and Representations - An Elementary Introduction. Brian C Hall
Lie Groups, an Approach Through Invariants adn Representations. Claudio Procesi
Continious Symmetries, Lie Algebras, Differential Equations, and Computer Algebra. Steeb Willihans

1.15 Numerical Methods

Intro with Matlab

Numerical Analysis (3rd ed). Timothy Sauer
Elementary Numerical Analysis (3rd ed). Atkinson, Han
Scientific Computing with MATLAB and Octave (4th ed). Quarteroni, Gervasio
Scientific Computing - An Introduction using MAPlE and MATLAB. Gander, Gander, Kwok
Exercises in Computational Mathematics with MATLAB. Lyche, Merrien

Intro with Python

Numerical Methods in Engineering with Python 3. Jaan Kiusalaas
Einfuehrung in die Numerik. Scheichl & Friess
Einfuehrung in die Numerik. Zech

Older Ref

Introduction to Applied Numerical Analysis. Hamming

1.16 Probability and Statistics

Probability

Core Track

Probability - An Introduction with Statistical Applications (2nd ed). John J Kinney
Introduction to Probability (2nd ed). Blitzstein, Hwang
Introduction to Probability. Anderson, Seppalainen, Valko
A Course in Probability (10th ed). Sheldon Ross
Probability with Applications in Engineering, Science, and Technology (2nd ed). Carlton, Devore
Introduction to Probability for Data Science. Stanley H Chan
Probability. Jim Pitman

Conceptual, Models, Problems

Understanding Probability. Tijms
Introduction to Probability Models (11th ed). Sheldon Ross
Probability Models (2nd ed). John Haigh

Problem Book Specific

Problems and Snapshots from the World of Probability. Blom, Holst, Sandell
40 Puzzles and Problems in Probability and Mathematical Statistics. Schwartz
Exercises in Probability. Cacoullos
The Pleasures of Probability. Richard Isaac

Proabibility of Games Specific

Games, Gambling, and Probability - An Introduction to Mathematics (2nd ed). David G Taylor
The Mathematics of Games and Gambling. Edward W Packel

Historical

Chance and Choice by Cardpack and Chessboard - An Introduction to Probability in Practice by Visual Aids. Lancelot Hogben
Statistical Theory - The Relationship of Probability, Credibility and Error. Lancelot Hogben

Multivariate Analysis & Lina for Statistics

Methods of Multivariate Analysis (3rd ed). Rencher, Christensen
Linear Algebra and Matrix Analysis for Statistics. Banerjee, Roy
Matrix Algebra From a Statistician’s Perspective. Harville
Matrix Algebra Useful for Statistics (2nd ed). Searle, Khuri

Statistics

Introductory

Probability and Statistics for Science & Engineering - with Examples in R. Hongshik Ahn
Introductory Statistics. Sheldon Ross
Discovering Statistics Using R. Field, Miles, Field
Modern Elementary Statistics (12th ed). Freund, Perles

Core Track

Probability and Statistics with R for Engineers and Scientists. Akritas
Introduction to Probability and Statistics for Engineers and Scientists (6th ed). Sheldon M Ross
Probability and Statistics - for Engineering and the Sciences (9th ed). Devore
Probability and Statistics (4th ed). DeGroot, Schervish
Statistics (4th ed). Freedman, Pisani, Purves

Mathmetical Statistics

An Introduction to Mathematical Statistics and Its Applications (5th ed). Larsen, Marx
Modern Mathematical Statistics with Applications (3rd ed). Devore, Berk, Carlton
Mathematical Statistics and Data Analysis. Rice
Introduction to Mathematical Statistics. Hogg, McKean, Craig

Data Science

Modern Data Science with R (2nd ed). Baumer, Kaplan, Horton
Modern Statisticsg with R - From Wrangling and Exploring Data to Inference and Predictive Modelling (2nd ed). Thulin
The Data Science Design Manual. Steven S Skiena
A Tour of Data Science - Learn Pytnon and R in Parallel. Zhang
Data Science Using Python and R. Larose
Intro to Python for Computer Science and Data Science. Deitel, Deitel
R for Data Science - Import, Tidy, Transform, Visualize and Model Data. Wickham, Cetinkaya-Rundel, Grolemund
Practical Data Science with R. Zumel, Mount

Older Books

Statistics for Technology - A Course in Applied Statistics (1978). Chatfield
Statistics for biologists. Finney
The Computation of Style. Kenny
Elementary Statistical Methods. Wetherill