Pure Mathematics for Beginners: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra
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Pure Mathematics for Beginners
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
22 reviews for Pure Mathematics for Beginners: A Rigorous Introduction to Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra
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William Camp –
Clear and concise
Al –
This is an excellent book for beginners who would like to learn what pure mathematics is. It is written in a simple, elegant,pleasant, and easy to read and follow way. Though it might be helpful to have a good high school math base, but does not need any deep math background.
The content:
1- is very engaging and any interested beginner would always wonder what s the next chapter will be.
2-Written in a way like building legos. The sequence of the chapters and the topics(ideas) in each chapter flow smoothly and logically.
3-All concepts and theorems are explained clearly and followed by plenty of examples.
4-All problems come with detailed solutions and extra explanations. Some problems are difficult and may require the reader to look at the solution which might need to be read once or twice to understand.
I had great pleasure learning and exploring the topics of pure mathematics from this book, and I highly recommended for beginners who are going to any undergrad major requiring pure math and for self-learners too. It may also serve as a reference for graduate students for a quick review.
Matheus Lobo –
Este é um dos livros mais didáticos de Matemática Pura que já estudei! As explicações (tanto da teoria como dos exemplos) são passo a passo. Recomendo para especialistas e não especialistas. O autor apresenta 8 áreas da Matemática Pura, com dois capítulos por área, um mais básico e outro mais avançado. Os capítulos introdutórios podem ser estudados de forma independente.
george b potter –
This truly outstanding book explains proofs, theory and structure of some of the most core areas of mathematics, and does so in a way that is clear, comprehensible and compelling. To do so in areas as complex and as abstract as these subjects are is no mean feat, but Dr. Warner makes it look easy. It is the best book I could have obtained as I am contemplating pursuing a Masters in math after receiving my bachelors degree over fifty years ago. This text provides me with a perfect vehicle for review and update. I rate it six stars out of a possible five!
Pedro F Lopez –
Finally, an excellent introduction into abstract/pure mathematics for nonmathematicians. This book fills an important niche for self learners who are interested in pure mathematics but feel that many of the so-called introductory text do not adequately explain the material for the beginner without additional guidance. The problem sets and their detailed solutions provide such a nuanced and profound understanding than I have been unable to find elsewhere. I look forward to more such books on other fundamental abstract mathematics topics from Dr. Warner such as analysis, abstract algebra, topology, etc.
Matheus Lobo –
Jose Ramon Abuin Requesens –
Libro nuevo resumen para matemáticos y físicos que se inician en estas lides.
John Redcross –
This book was very useful for understanding the mathematics used in proving theorems in the mathematical treatments of quantum mechanics. The book is great for self study since it provides clear and thorough solutions to the problems which can be consulted after working through the problems on your own.
baggins65 –
Crossing over to pure math is weird for a lay person like me, this book does an excellent job of introducing abstract concepts without to many tears.
RC –
This book is great. Excellent introduction to the topics covered. Straight to the point. Nice notes about proofs and theorems. Great illustrations. Clear and concise. I do not have enough words to describe how helpful this book was to me.
Greg Larsen –
This is an exceptionally good book, and one of the best I’ve ever seen for self-study. The content, overall structure and clarity of explanation is superior.
The first two chapters on logic and set theory provide a solid foundation for the rest of the topics in the book, and for all of mathematics. The problem sets gradually increase in difficulty, and combined with fully explained solutions, enable a real understanding of the material. I also like that he explains how to think about certain concepts and how proof techniques and solution writing is included – highly recommend!
Cathy lee –
Great book proofs and therms
Erik Buehler –
The solution set can be downloaded via a link at the top of the page of each set of problems. I puzzled over how to get the solutions before diving into the book, and then noticed the link at the top of the page. I thought someone else might find this helpful prior to buying.
Robert F. Barnes –
THANKS!!!
BOZ –
Great introduction for high school students and first year undergrads
George –
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.
C. G. Hanwella –
A well written introductory book suitable for Undergratuate first year students. Very suitable for self study without the aid of a Tutor.
Mark Karavan –
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.
jose –
The proofs have every detail
Kevin Morris –
Excellent introduction. Simple, straightforward presentation that requires some effort to digest but all of the requisite information is delivered clearly and concisely.
Rex –
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.
new_york_reader10 –
clear, to the point, does exactly what it states it will do. no fluff.