Pure Mathematics for Beginners consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra. The 16 lessons in this book cover basic through intermediate material from each of these 8 topics. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Pure Mathematics for Beginners is perfect for
professors teaching an introductory college course in higher mathematics
high school teachers working with advanced math students
students wishing to see the type of mathematics they would be exposed to as a math major.
The material in this pure math book includes:
16 lessons in 8 subject areas.
A problem set after each lesson arranged by difficulty level.
A complete solution guide is included as a downloadable PDF file.
Pure Math Book Table Of Contents (Selected)
Here’s a selection from the table of contents:Introduction
Lesson 1 – Logic: Statements and Truth
Lesson 2 – Set Theory: Sets and Subsets
Lesson 3 – Abstract Algebra: Semigroups, Monoids, and Groups
Lesson 4 – Number Theory: Ring of Integers
Lesson 5 – Real Analysis: The Complete Ordered Field of Reals
Lesson 6 – Topology: The Topology of R
Lesson 7 – Complex Analysis: The Field of Complex Numbers
Lesson 8 – Linear Algebra: Vector Spaces
Lesson 9 – Logic: Logical Arguments
Lesson 10 – Set Theory: Relations and Functions
Lesson 11 – Abstract Algebra: Structures and Homomorphisms
Lesson 12 – Number Theory: Primes, GCD, and LCM
Lesson 13 – Real Analysis: Limits and Continuity
Lesson 14 – Topology: Spaces and Homeomorphisms
Lesson 15 – Complex Analysis: Complex Valued Functions
Lesson 16 – Linear Algebra: Linear Transformations
Reviews (5)
5 reviews for Pure Mathematics for Beginners: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex…
Rex
Rated 5 out of 5
October 14, 2022
I am about half way through this book at the moment and it has definitely taught me a lot. The explanations are clear, concise and direct. The excerci...More
I am about half way through this book at the moment and it has definitely taught me a lot. The explanations are clear, concise and direct. The excercise questions are graded from easier to more difficult, so you can approach the work from your own personal level of understanding. I would recommend this for a beginner to pure mathematics as some of the other books I have read are not as direct. This seems definitely more condensed and to the point and thus holds your focus more intently. Happy with the purchase.
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jose
Rated 5 out of 5
April 4, 2020
The proofs have every detail
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MKaravan
Rated 5 out of 5
December 15, 2019
This is one of the best books I've ever purchased. It helped give me a strong foundation in math, one that I could not get from discrete maths (I'm in...More
This is one of the best books I've ever purchased. It helped give me a strong foundation in math, one that I could not get from discrete maths (I'm in computer science).
This book is rigorous. In fact, it is pure rigor. It is 200 pages of formal definitions, proofs and problems. There is very little to help you with intuition. However, if you supplement this book with lots of YouTube videos, this is not a problem. Please be advised that you will have to do this if you are an intuitive learner.
The quizzes are excellent. ALL of the questions have online answers (as opposed to selected questions, which you will often find in math textbooks). The author is very elaborate with them.
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CHanwella
Rated 5 out of 5
November 25, 2019
A well written introductory book suitable for Undergratuate first year students. Very suitable for self study without the aid of a Tutor.
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George
Rated 5 out of 5
October 3, 2019
Great introduction to most undergraduate math classes. Kind of like a cliff notes or for Dummies series, where it gives general idea. Has been a great...More
Great introduction to most undergraduate math classes. Kind of like a cliff notes or for Dummies series, where it gives general idea. Has been a great quick reference book.
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This book is rigorous. In fact, it is pure rigor. It is 200 pages of formal definitions, proofs and problems. There is very little to help you with intuition. However, if you supplement this book with lots of YouTube videos, this is not a problem. Please be advised that you will have to do this if you are an intuitive learner.
The quizzes are excellent. ALL of the questions have online answers (as opposed to selected questions, which you will often find in math textbooks). The author is very elaborate with them.