Mathematical Induction 101: With 101 Practice Problems

Description

This book starts with a brief introduction of mathematical induction and provides 101 practice problems of mathematical induction proofs. The problems have various levels of difficulty and cover a wide range of topics - sequences, series, products, inequality, trigonometry, floor function, derivatives, integrals, matrices, set theory, etc. Those who want to learn about mathematical induction can learn from this book, and those who are already familiar with mathematical induction can find some fun problems to practice.Reviews"In the ideal situation, every college student should learn some mathematics, with the depth and difficulty largely varying. As in the practice of most refined universities, mathematical education should never be standardized. Meanwhile, math induction is one of the key tools that students need to know. Based on my teaching experiences to many Chinese and international students, I found Tran’s book fairly interesting and accessible. Mathematical Induction 101 contains 101 carefully chosen exercise problems. I believe that Tran’s book will prove to be useful for college students in the broad range of arts and sciences. Hopefully many will appreciate the beauty and power of mathematical reasoning with mastery of math induction after using this book." - Prof. Chunwei Song, Peking University"This book provides an interesting collection of identities and inequalities that can be proved by mathematical induction. These 101 practices will be useful to learn standard techniques. Some of the topics and their solutions would also be found stimulating even for advanced students of mathematics." - Prof. Hiroaki Nakamura, Osaka University"This book provides almost all types of problems in high school and collegiate mathematics which can be solved by mathematical induction. To each problem, a self-contained and detailed solution is given. Difficulty ranges from quite elementary to somewhat complex. Among them there are many interesting ones. I am particularly interested in problems related to the Fibonacci sequence, floor function, and iterated functions." - Prof. Emeritus Young-One Kim, Seoul National University"As a mathematics student, this is a book I would have loved in my introductory proof class. Duc Van Khanh Tran has written up a fantastic way to both learn and practice one of the most essential tools in a mathematician's toolkit: Induction!It's difficult to find such a large, comprehensive array of well-written and demonstrative practice problems, which makes this all the more valuable a resource. Duc Van Khanh Tran carefully pens each solution to be as intuitive and explanatory as possible, so the risk of confusion at a solution is minimal.The vast amount of problems is complemented by the vast array of topics the book covers. Inequalities, sequences, trigonometry, power series, derivatives, and integrals are only some of the concepts found, guaranteeing that anyone interested in math will get something new out of this book. I've tried a few of these for fun! I really like the integral problems myself.All in all, if you'd like to learn about induction, hone your induction skills, or just want a bunch of fun induction problems, purchase away! You won't regret it!" - Said Kaili, Undergraduate Student of Mathematics, University of Virginia"Despite minimal prior proof background, I can grasp the main scopes of the book without much difficulty. Indeed, Duc Tran’s book provides clear instructions, comprehensive content, and helpful problems that ease students into learning mathematical induction." - Ky Minh Vinh Nguyen, Undergraduate Student of Informatics, University of Texas at Austin