Exploring Mathematics: Problem-Solving and Proof
Have you ever faced a mathematical problem and had no idea howto approach it? Or perhaps you had an idea but got stuck halfwaythrough? This book guides you in developing your creativity, as ittakes you on a voyage of discovery into mathematics.Readers will not only learn strategies for solving problems andlogical reasoning, but they will also learn about the importance ofproofs and various proof techniques. Other topics covered includerecursion, mathematical induction, graphs, counting, elementarynumber theory, and the pigeonhole, extremal and invarianceprinciples. Designed to help students make the transition fromsecondary school to university level, this book provides readerswith a refreshing look at mathematics and deep insights intouniversal principles that are valuable far beyond the scope of thisbook.Aimed especially at undergraduate and secondary school students aswell as teachers, this book will appeal to anyone interested inmathematics. Only basic secondary school mathematics is required,including an understanding of numbers and elementary geometry, butno calculus. Including numerous exercises, with hints provided,this textbook is suitable for self-study and use alongside lecturecourses.