Books for beginning to learn Pure Mathematics

In summary, the conversation discusses the individual's search for texts to learn abstract/pure mathematics, specifically focusing on linear algebra and proof-writing skills. Some recommended books are A Concise Introduction to Pure Mathematics by Martin Liebeck, Chapter Zero: Fundamental Notions of Abstract Mathematics by Carol Schumacher, The Nuts and Bolts of Proofs by Antonella Cupillari, and How to Prove It: A Structured Approach. The individual also asks for additional book suggestions to help with their current interests and goals.
  • #1
For a while now I have been looking for a series of texts that I can read in order to learn some of the basics of abstract/pure mathematics. I am currently taking Calculus II with Stewart's book as my text, and this summer I plan on going through Spivak's Calculus.

I have finished my universities Linear Algebra 1 but I do not feel satisfied with the understanding I left with ( the class was a bit "light" but also me neglecting the need for a true understanding didn't help ). I would like to work through Linear Algebra Done Right by Sheldon Axler also.

I need help developing my skills at constructing proofs before I start Spivak's book. Before I do that though I would like to get some other books under my belt.

Right now I am looking at:

A Concise Introduction to Pure Mathematics - Martin Liebeck

It is meets all my criteria for what I want except there is no solution manual to be found, this is a problem as I am going to be self-studying. I have only read a bit of it and it seems alright, besides the constant uncertainty when I solve a problem.

Another book I have been looking at is
Chapter Zero : Fundamental Notions of Abstract Mathematics - Carol Schumacher

It seems like a bit much for me to jump into though I think I could handle it if I gave it some time. A instructor at my university has a set of lecture notes that "sort of" accompany it, so that might help. I can not seem to find a solution manual to this also, another problem.

A book on Proofs I have been looking at is :

The Nuts and Bolts of Proofs - Antonella Cupillari

This book seems pretty good but I would like to do/read a bit more set theory and logic before starting it. Although it does seem manageable. It has detailed solutions in the book itself, which is a large plus.

This also seems to be along the lines of what I am looking for :

How to Prove It: A Structured Approach

I have yet to actually hold the book and look through it, I am also unsure if there are solutions out there for it.

I would really appreciate suggestions on books that encompass my current interests anything that will help me get started with pure mathematics. Specifically develop my skills at writing proofs, and obviously some of the prerequisite fundamentals needed to write them.

My current pre-occupation with desiring ( needing?) a solution manual for "security" may be holding me back, but any texts you could recommend would be greatly appreciated.
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  • #2
Not sure about the others, but "How to prove it" is a wonderful book. I don't know if there is a solution manual, but I think there are enough examples in the book to get the point through.
  • #3
Velleman's book is good, but I often found it slow when I was trying to learn how to do proofs. Therefore I recommend complementing it with a nippier book like this one:

1. What is the best book for beginners to learn Pure Mathematics?

The best book for beginners to learn Pure Mathematics is subjective and may vary depending on individual learning styles and goals. Some popular options include "A First Course in Abstract Algebra" by John B. Fraleigh, "Introduction to Real Analysis" by Robert G. Bartle and Donald R. Sherbert, and "Linear Algebra: A Modern Introduction" by David Poole.

2. Do I need any prior knowledge or background in mathematics to start learning Pure Mathematics?

While prior knowledge in basic algebra and geometry may be helpful, it is not necessary to have a deep understanding of mathematics to begin learning Pure Mathematics. These books are designed for beginners and will cover the necessary foundations.

3. How long does it take to learn Pure Mathematics?

The time it takes to learn Pure Mathematics varies depending on the individual's dedication and effort put into studying. It can take anywhere from a few months to a year or more to gain a solid understanding of the basics.

4. Are there any online resources or videos that can supplement my learning from the book?

Yes, there are many online resources and videos that can supplement your learning from the book. Some popular ones include Khan Academy, MIT OpenCourseWare, and YouTube channels such as 3Blue1Brown and MathTheBeautiful.

5. Can I self-study Pure Mathematics or do I need a tutor or instructor?

It is possible to self-study Pure Mathematics with the help of books and online resources, but having a tutor or instructor can provide valuable guidance and feedback. It is recommended to seek assistance if you encounter difficulties or have specific questions.

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