Bogumił Kamiński - Train Your Brain: Challenging Yet Elementary Mathematics

Train Your Brain

Series editors:

Al Boggess, Kenneth H. Rosen

Nonlinear Optimization

Models and Applications

William P. Fox

Linear Algebra

James R. Kirkwood, Bessie H. Kirkwood

Real Analysis

With Proof Strategies

Daniel W. Cunningham

Train Your Brain

Challenging Yet Elementary Mathematics

Bogumi Kamiski, Pawe Praat

Contemporary Abstract Algebra, Tenth Edition

Joseph A. Gallian

Geometry and Its Applications

Walter J. Meyer

Linear Algebra

What you Need to Know

Hugo J. Woerdeman

Introduction to Real Analysis, 3rd Edition

Manfred Stoll

Discovering Dynamical Systems Through Experiment and Inquiry

Thomas LoFaro, Jeff Ford

Functional Linear Algebra

Hannah Robbins

https://www.routledge.com/Textbooks-in-Mathematics/book-series/CANDHTEXBOOMTH

First edition published 2020

by CRC Press

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ISBN: 978-0-367-56487-2 (pbk)

ISBN: 978-1-003-09798-3 (ebk)

ISBN: 978-0-367-67935-4 (hbk)

Typeset in Computer Modern font

by KnowledgeWorks Global Ltd.

The book contains carefully selected problems that are challenging, yet only require elementary mathematics. It is intended to prepare the readers for rigorous mathematics, but neither prior preparation nor any mathematical sophistication is required from them before reading this book. The book guides the readers to think and express themselves in a rigorous, mathematical way, to extract facts, analyze the problem, and identify main challenges. Moreover, it shows how to draw appropriate, true conclusions and helps to see a big picture. Despite the fact that this is not the main goal of this book, as a bi-product, the readers are provided with a firm foundation in a diverse range of topics that might be useful in their future work. Finally, we often use computer support to help us get a better intuition into discussed problems. This is a still rather unique approach in mathematics but is getting more and more popular in the current multidisciplinary and data driven world.

The presented material can be seen as a means to bridge the gap between introductory calculus/linear algebra courses and more advanced courses that are offered at universities. It improves the ability to read, write, and think in a rigorous, mature mathematical fashion. It provides a solid foundation of various topics that would be useful for more advanced courses. However, the book is not only intended for undergraduate students that would like to become professional research mathematicians. In almost any mathematically related work (such as computer programming, data science, machine learning, economics, engineering, etc.), precise reasoning, and understanding what logical steps need to be taken to transition from the assumptions to the desired conclusion, are crucial to be successful.