Exploring Mathematics: Problem-Solving and Proof

Daniel Grieser

Have you ever been presented with a mathematical problem and been completely at a loss as to how to solve it? Or maybe you had a concept but got stuck in the middle of implementing it. This book will help you enhance your creative abilities while also leading you on an adventure of discovery into the world of mathematics.

Not only will readers acquire skills for logical thinking and problem-solving tactics, but they will also gain an understanding of the significance of proofs and various proof methodologies. Recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal, and invariance principles are other topics covered in this course. This book offers readers a fresh perspective on mathematics and profound insights into universal principles that are useful well beyond the scope of this book. The book was written to assist students in making the transition from secondary school to university-level education.

This book is written with college and secondary school students as well as teachers in mind, but anyone who has an interest in mathematics will find it to be an enjoyable read. Calculus is not necessary; rather, only the fundamental mathematical concepts taught in secondary school must be understood. These concepts include numbers and elementary geometry. This textbook is appropriate for independent study and usage in conjunction with classroom instruction because it has many exercises that come with detailed explanations.