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sethuraman b proofs ideas prelude advanced math 2022

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Textbook in PDF format Proofs and Ideas serves as a gentle introduction to advanced mathematics for students who previously have not had extensive exposure to proofs. It is intended to ease the student's transition from algorithmic mathematics to the world of mathematics that is built around proofs and concepts. The spirit of the book is that the basic tools of abstract mathematics are best developed in context and that creativity and imagination are at the core of mathematics. So, while the book has chapters on statements and sets and functions and induction, the bulk of the book focuses on core mathematical ideas and on developing intuition. Along with chapters on elementary combinatorics and beginning number theory, this book contains introductory chapters on real analysis, group theory, and graph theory that serve as gentle first exposures to their respective areas. The book contains hundreds of exercises, both routine and non-routine. This book has been used for a transition to advanced mathematics courses at California State University, Northridge, as well as for a general education course on mathematical reasoning at Krea University, India. Introduction The Pigeonhole Principle Statements Counting, Combinations Sets and Functions Interlude: So, How to Prove It? An Essay Induction Cardinality of Sets Equivalence Relations Unique Prime Factorization in the Integers Sequences, Series, Continuity, Limits The Completeness of ℝ Groups and Symmetry Graphs: An Introduction

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Sethuraman B. Proofs and Ideas. A Prelude to Advanced Math. 2022.pdf 21.2 MB

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sethuraman b proofs ideas prelude advanced math 2022