Pure Mathematics For Pre Beginners Pdf

Book Name: Pure Mathematics for Beginners
Author: Dr. Steve Warner
Pages: 262
Size: 11 MB

This book was written to provide a basic but rigorous introduction to pure mathematics, while exposing students to a wide range of mathematical topics in logic, set theory, abstract algebra, number theory, real analysis, topology, complex analysis, and linear algebra. For students: There are no prerequisites for this book. The content is completely self-contained. Students with a bit of mathematical knowledge may have an easier time getting through some of the material, but no such knowledge is necessary to read this book.

Pure Mathematics for Beginners Pdf Download

More important than mathematical knowledge is "mathematical maturity." Although there is no single agreed upon definition of mathematical maturity, one reasonable way to define it is as "one's ability to analyze, understand, and communicate mathematics." A student with a higher level of mathematical maturity will be able to move through this book more quickly than a student with a lower level of mathematical maturity. Whether your level of mathematical maturity is low or high, if you are just starting out in pure mathematics, then you're in the right place. If you read this book the "right way," then your level of mathematical maturity will continually be increasing.

This increased level of mathematical maturity will not only help you to succeed in advanced math courses, but it will improve your general problem solving and reasoning skills. This will make it easier to improve your performance in college, in your professional life, and on standardized tests such as the SAT, ACT, GRE, and GMAT. So, what is the "right way" to read this book? Simply reading each lesson from end to end without any further thought and analysis is not the best way to read the book. You will need to put in some effort to have the best chance of absorbing and retaining the material. When a new theorem is presented, don't just jump right to the proof and read it. Think about what the theorem is saying. Try to describe it in your own words. Do you believe that it is true? If you do believe it, can you give a convincing argument that it is true?

If you do not believe that it is true, try to come up with an example that shows it is false, and then figure out why your example does not contradict the theorem. Pick up a pen or pencil. Draw some pictures, come up with your own examples, and try to write your own proof. You may find that this book goes into more detail than other math books when explaining examples, discussing concepts, and proving theorems. This was done so that any student can read this book, and not just students that are naturally gifted in mathematics. So, it is up to you as the student to try to answer questions before they are answered for you. When a new definition is given, try to think of your own examples before looking at those presented in the book. And when the book provides an example, do not just accept that it satisfies the given definition. Convince yourself. Prove it.

Pure Mathematics for Beginners Pdf Download

Each lesson is followed by a Problem Set. The problems in each Problem Set have been organized into five levels, Level 1 problems being considered the easiest, and Level 5 problems being considered the most difficult. If you want to get just a small taste of pure mathematics, then you can work on the easier problems. If you want to achieve a deeper understanding of the material, take some time to struggle with the harder problems. 8 For instructors: This book can be used for a wide range of courses. Although the lessons can be taught in the order presented, they do not need to be.

The lessons cycle twice among eight subject areas: logic, set theory, abstract algebra, number theory, real analysis, topology, complex analysis, and linear algebra. Lessons 1 through 8 give only the most basic material in each of these subjects. Therefore, an instructor that wants to give a brief glimpse into a wide variety of topics might want to cover just the first eight lessons in their course. Lessons 9 through 16 cover material in each subject area that the author believes is fundamental to a deep understanding of that particular subject. For a first course in higher mathematics, a high-quality curriculum can be created by choosing among the 16 lessons contained in this book. As an example, an introductory course focusing on logic, set theory, and real analysis might cover Lessons 1, 2, 5, 9, 10, and 13.

Lessons 1 and 9 cover basic sentential logic and proof theory, Lessons 2 and 10 cover basic set theory including relations, functions, and equinumerosity, and Lessons 5 and 13 cover basic real analysis up through a rigorous treatment of limits and continuity. The first three lessons are quite basic, while the latter three lessons are at an intermediate level. Instructors that do not like the idea of leaving a topic and then coming back to it later can cover the lessons in the following order without issue: 1, 9, 2, 10, 5, and 13. As another example, a course focusing on algebraic structures might cover Lessons 2, 3, 4, 5, 10, and 11. As mentioned in the previous paragraph, Lessons 2 and 10 cover basic set theory. In addition, Lessons 3, 4, 5, and 11 cover semigroups, monoids, groups, rings, and fields. Lesson 4, in addition to a preliminary discussion on rings, also covers divisibility and the principle of mathematical induction. Similarly, Lesson 5, in addition to a preliminary discussion on fields, provides a development of the complete ordered field of real numbers. These topics can be included or omitted, as desired. Instructors that would also like to incorporate vector spaces can include part or all of Lesson 8. The author strongly recommends covering Lesson 2 in any introductory pure math course.

This lesson fixes some basic set theoretical notation that is used throughout the book and includes some important exposition to help students develop strong proof writing skills as quickly as possible. The author welcomes all feedback from instructors. Any suggestions will be considered for future editions of the book. The author would also love to hear about the various courses that are created using these lessons.

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