Undergraduate Level Math Book Recommendations

Highly Recommended Math Books for University Self Study

Recently, a viewer of my website asked if I was able to suggest any undergraduate level university textbooks for self study that follows the university curriculum.

Self-study is challenging but not impossible. Choosing a good and appropriate book of the right level is of crucial importance. For instance, for beginners to Calculus, I wouldn’t recommend Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics) by Rudin. It is simply too difficult for beginners or even intermediate students. Any book by Bourbaki is also not suitable for beginners, for instance.

Update: I recently found a book that is a better alternative to Rudin: Mathematical Analysis, Second Edition by Apostol! Many online sources have very positive reviews on Apostol’s Analysis book. I have read it and found it much more readable than Rudin.

I would like to suggest the following books (mainly for Pure Mathematics). Ideally, the motivated student is able to self study and obtain the knowledge equivalent to a 4 Year course at a university.

The recommendations are divided into Year 1, Year 2, Year 3 and Year 4.

If you have any other recommendations, please feel free to comment below!

Year 1

Introduction to Pure Math and Proofs:

How to Prove It: A Structured Approach


Thomas’ Calculus (12th Edition)

Linear Algebra:

Linear Algebra and Its Applications, 4th Edition

Multivariable Calculus:

Thomas’ Calculus, Multivariable (13th Edition)

Year 2

Linear Algebra II (Second Year Course):

Linear Algebra, 4th Edition

Analysis I: 

Introduction to Real Analysis

Abstract Algebra I:

A First Course in Abstract Algebra (3rd Edition)

This book will be an introduction to Group Theory.


Introduction to Probability, 2nd Edition

Analysis II:

Calculus, 4th edition

(Note: Despite the title “Calculus”, this book is actually a rather rigorous book on Analysis, suitable as a second course textbook)

Complex Analysis I:

Complex Variables and Applications (Brown and Churchill)

Year 3

Analysis III:

Introductory Real Analysis (Dover Books on Mathematics)

ODE (Ordinary Differential Equations):

Ordinary Differential Equations (Dover Books on Mathematics)

Graph Theory:

A First Course in Graph Theory (Dover Books on Mathematics)

Algebra II:

Abstract Algebra, 3rd Edition

Algebra II will usually be a course on Rings, Modules.

(Note: You can use this book for learning Galois Theory too)

Differential Geometry:

Differential Geometry of Curves and Surfaces

Year 4 

Number Theory:

An Introduction to the Theory of Numbers

Galois Theory:

Abstract Algebra, 3rd Edition

(Note: Same textbook as for Algebra II)

PDE (Partial Differential Equations):

A First Course in Partial Differential Equations: with Complex Variables and Transform Methods (Dover Books on Mathematics)


A Beginner’s Guide to Mathematical Logic (Dover Books on Mathematics)

Functional Analysis:

Introductory Functional Analysis with Applications


Topology (2nd Edition)

(Note: See also my book review on Topology by Munkres)

Measure and Integration:

The Elements of Integration and Lebesgue Measure

Congratulations for reaching the bottom of this long list!

All the best for your studies in Mathematics. 🙂

About mathtuition88

This entry was posted in math tuition, maths tuition and tagged , . Bookmark the permalink.

25 Responses to Undergraduate Level Math Book Recommendations

  1. Pingback: Math Teachers at Play #79 | Let's Play Math!

  2. Pingback: Lee Kuan Yew was the Best Student in Mathematics in Raffles College | Singapore Maths Tuition

  3. Pingback: Xinmin Secondary 2010 Prelim Paper I Q24 Solution (Challenging/Difficult Probability O Level Question) | Singapore Maths Tuition

  4. Pingback: Measure and Integration Recommended Book | Singapore Maths Tuition

  5. Pingback: A nonnegative function f in M(X,X) is the limit of a monotone increasing sequence in M(X,X) | Singapore Maths Tuition

  6. Pingback: Aut(Z_n): Automorphism Group of Z_n | Singapore Maths Tuition

  7. Pingback: Proof that any subgroup of index 2 is normal | Singapore Maths Tuition

  8. Pingback: Video on Computing Homology Groups | Singapore Maths Tuition

  9. Pingback: Definition of Euclidean Domain and Principal Ideal Domain (PID) | Singapore Maths Tuition

  10. Pingback: Z[Sqrt(-2)] is a Principal Ideal Domain Proof | Singapore Maths Tuition

  11. Pingback: If Ratio Test Limit exists, then Root Test Limit exists, and both are equal | Singapore Maths Tuition

  12. Pingback: Weierstrass M-test Proof and Special Case of Abel’s Theorem | Singapore Maths Tuition

  13. Pingback: Cycle Decomposition of Permutations is Unique | Singapore Maths Tuition

  14. Pingback: Geometric n-simplex is convex | Singapore Maths Tuition

  15. Pingback: Zmn/Zm isomorphic to Zn | Singapore Maths Tuition

  16. Pingback: Proof of Wilson’s Theorem using Sylow’s Theorem | Singapore Maths Tuition

  17. Pingback: |HK|=|H||K|/|H intersect K| | Singapore Maths Tuition

  18. Pingback: Interpolation Technique in Analysis | Singapore Maths Tuition

  19. Pingback: Merry Christmas | Singapore Maths Tuition

  20. Pingback: Recommended Functional Analysis Book (Graduate Level) | Singapore Maths Tuition

  21. Pingback: Further Maths Versus H2 Maths | Singapore Maths Tuition

  22. Pingback: Calculate Ranking Points JC | Singapore Maths Tuition

  23. Pingback: Wheeden Zygmund Measure and Integration Solutions | Singapore Maths Tuition

  24. Pingback: Book Review: Topology, James R. Munkres | Singapore Maths Tuition

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.