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Undergraduate Math Curriculum
Free undergraduate math curriculum
Free mathematics curriculum aiming to replicate an undergraduate degree in math using Open Education Resources/OpenCourseWare/MOOCs.
Go Ham
- Archive.org - Math Folkscanomy
- Pickover, Clifford - Passion For Mathematics
- Struik, Dirk - A Concise History of Mathematics
- Gardner, Martin - The Colossal Book of Mathematics
- Developer-Y/math-science-video-lectures
- EbookFoundation/free-science-books
- Science Books Online - Math
- American Institute of Mathematics - Open Textbook Initiative
- EMich - Mathematics & Statistics
- Sacred Heart OER Resource - Math
Basics
- Khan Academy - Mathematics
- OpenStax - Math textbooks
- Zakon, Elias - Basic Concepts of Mathematics
- LibreTexts - Math
- Student calculator math - Oliva, Ralph A; LaMont, M. Dean; Fowler, Linda R;
]
Calculus I
- OpenStax - Calc I
- Spivak - Calculus
- Saylor.org - MA005: Calculus 1
- Elementary Calculus: An Infinitesimal Approach - H. Jerome Keisler
- Holm, Tara - Mathematics for Computer Science
- Calculus - Gilbert Strang
- Calculus - MIT OpenCourseWare
- Sloughter, Dan - Yet Another Calculus Text
- Sloughter, Dan - Difference Equations to Differential Equations
- Apostol, Tom - Calculus Vol. 1
Calculus II
Calculus III
- OpenStax - Calc III
- Sloughter, Dan - The Calculus of Functions of Several Variables
- Saylor.org - MA103: Multivariable Calculus
- MIT OCW - Multivariable Calculus
- Hubbard, J. H.; Hubbard, B. B. - Vector Calculus Linear Algebra And Differential Forms A Unified Approach
Differential Equations
- Fields, Joe - A Gentle Introduction to the Art of Mathematics
- Learn Differential Equations: Tutorials with Gilbert Strang and Cleve Moler
- Saylor.org - MA221: Differential Equations
- Saylor.org - MA222: Introduction to Partial Differential Equations
- MIT OCW - Calculus with Applications
- MIT OCW - Differential Equations
- Schaum's Theory & Problems of Differential Equations
Formal Logic
- Magnus, P.D. - forallx: An Introduction to Formal Logic
- Saylor.org - MA111: Introduction to Mathematical Reasoning
- Saylor.org - MA201: Mathematical Logic and Theory of Computation
Discrete Mathematics for Computer Science
- MIT OCW - Mathematics for Computer Science (Fall 2010)
- MIT OCW - Mathematics for Computer Science (Spring 2015)]
- ADU - Discrete Mathematics
- Knuth, Donald - Concrete Mathematics
- Little #96D7AF Books/#Discrete-Mathematics
Algorithms
Discrete Mathematics
- Hammack, Richard - Book of Proof
- Kwong, Harris - A Spiral Workbook for Discrete Mathematics
- Doerr, Al and Levasseur, Ken - Applied Discrete Stuctures
- Naive set theory by Halmos, Paul
Linear Algebra
- Beezer, Robert - A First Course in Linear Algebra
- Saylor.org - MA211: Linear Algebra
- Saylor.org - MA212: Linear Algebra II
- MIT OCW - Linear Algebra
- Linear algebra problem book by Halmos, Paul
- Schaum's Theory & Problems of Linear Algebra
Numerical Analysis
- Saylor.org - MA213: Numerical Analysis
- Ökten, G - First Semester in Numerical Analysis with Julia
- Elementary Numerical Analysis
- MIT - Lecture Notes
Applied Statistics
- OpenStax - Introductory Statistics
- LibreTexts - Statistics
- Boundless - Statistics
- Saylor.org - MA121: Introduction to Statistics
- Saylor.org - MA251: Statistics II
- MIT OCW - Statistics for Applications
Combinatorics
- Keller, MItchel and Trotter, William - Applied Combinatorics
- Bogart, Kenneth - Combinatorics Through Guided Discovery
- Morris, Joy - Combinatorics
Mathematical Statistics I
- ADU - Applied Probability
- Saylor.org - MA252: Introduction to Probability Theory
- Grinstead, Charles and Snell, J. Laurie - Introduction to Probability
- Little #96D7AF Books/#Statistics
Abstract Algebra
- Fraleigh - A first course in abstract algebra
- Connell, Edward - Elements of Abstract and Linear Algebra
- Judson, Thomas; Beezer, Rob; Mitchell, Lon - Abstract Algebra - Theory and Applications
- Saylor.org - MA231: Abstract Algebra I
- Saylor.org - MA232: Abstract Algebra II
- Harvard - Mathematics 122 - Abstract Algebra
- LaLonde, Scott - Notes on Abstract Algebra
Number Theory
- Saylor.org - MA233: Elementary Number Theory
- Moser, Leo - An Introduction to the Theory of Numbers
- Shoup, Victor - A Computational Introduction to Number Theory and Algebra
- Poritz, Jonathan - Yet Another Introductory Number Theory Textbook (Cryptology Emphasis Version)
- Apostol, Tom - Introduction to analytic number theory
- Hatcher, Allen - Topology of Numbers
Real Analysis I
- Bartle, Robert and Sherbert, Donald - Introduction to real analysis
- Rudin, Walter and Cooke, R - Principles Of Mathematical Analysis
- Sloughter, Dan - A Primer of Real Analysis
- Feinstein, Joel - Definitions, Proofs and Examples
- Zakon, Elias - Mathematical Analysis I
- Saylor.org - MA241: Real Analysis I
- Boman, Eugene and Rogers, Robert - How We Got from There to Here: A Story of Real Analysis
- Apostol, Tom - Mathematical analysis; a modern approach to advanced calculus
- Gelbaum, Bernard - Problems in analysis
- Stromberg and Hewitt - Real and abstract analysis : a modern treatment of the theory of functions of a real variable
- Abbott, Stephen - Understanding analysis
Real Analysis II
Mathematical Logic
Applied Mathematics
Functional Analysis
- Feinstein, Joel - Functional Analysis
- TUDelft - Stochastic Evolution Equations
- Rudin, Walter - Functional Analysis (version 2)
Complex Systems
Complex Analysis
- Rudin, Walter - Real and complex analysis
- Saylor.org - MA243: Complex Analysis
- Complex Numbers with Mathematica: Complex Arithmetic, Methods, and Geometric Interpretations
- Introductory Complex Analysis with Bill Kinney
- Analysis of a Complex Kind
- Nesse, William - Introduction to Applied Complex Variables
- Advanced Complex Analysis I
- Advanced Complex Analysis II
Category Systems
MATLAB
Math for Machine Learning
- MIT OCW - Matrix Methods in Data Analysis, Signal Processing, and Machine Learning
- functionalcs - Math Background for ML
Math for Finance
- Fahim, Arash - Introduction to Financial Mathematics
- MIT OCW - Topics in Mathematics with Applications in Finance
Topology
- Morris, Sidney - Topology Without Tears
- Munkres, James - Topology, a first course
- Hatcher, Allen - Algebraic Topology
- Kelley, John - General Topology
- Armstrong, M. A. - Basic topology
- Willard, Stephen - General topology
- Dugundji, James - Topology
- Schaum's Theory & Problems of General Topology
Misc
- Gelbaum, Bernard - Theorems and counterexamples in mathematics
- Mathematics : people, problems, results - vol1 vol2 vol3
Cheap Online Degrees
| Level | College | Est. Price |
|---|---|---|
| Undergrad | University of London - Data Science and Business Analytics | ~$7-8,000, 3-6 years |
| Undergrad | University of London - Mathematics and Economics | ~$7-8,000, 3-6 years |
| Undergrad | Open University - Mathematics & Statistics | ~$22,000 over 3-11 years |
| Masters | University of London - Graduate Mathematics | ~$2000 |
| Masters | Emporia State University - Graduate Mathematics |
