Essential Mathematics for Undergraduates: A Guided Approach to Algebra, Geometry, Topology and Analysis

This textbook covers undergraduate mathematics in abstract algebra, geometry, topology, and analysis, connecting key ideas and avoiding mechanical problem-solving. It is accessible to undergraduates and focuses on didactical learning, with examples and exercises. It is valuable for students and teachers alike.

Format: Hardback
Length: 490 pages
Publication date: 17 February 2022
Publisher: Springer Nature Switzerland AG

This comprehensive textbook delves into the realms of undergraduate mathematics, encompassing abstract algebra, geometry, topology, and analysis. Its primary objective is to establish a strong connection between the fundamental key ideas that underpin these diverse subjects. By providing guidance to STEM students, this text aims to enhance their knowledge and skills, thereby enriching their scientific education. It endeavors to steer clear of the conventional mechanical approach to problem-solving, which relies on the repetitive application of dry formulas. Throughout, the presentation maintains a rigorous mathematical rigor while remaining accessible to undergraduates.

The didactical focus permeates the various topics, evident in the book's structured layout. Part 1 serves as an introduction to the mathematical language and its principles, while Part 2 explores the number systems commonly used in practice. Part 3 focuses on developing the necessary backgrounds to solve equations and inequalities. Part 4 boldly breaks down the traditional boundaries between these areas, particularly emphasizing the interplay between algebra and geometry. Two appendices, Part 5, provide valuable supplementary material: the Greek etymology of frequently used terms and a comprehensive list of mathematicians mentioned in the book.

To facilitate learning, abundant examples and exercises are dispersed throughout the text. These resources not only enhance the understanding of the material but also encourage independent work. Students embarking on their undergraduate journey or seeking to supplement their existing knowledge will find this textbook an invaluable resource. Teachers can also utilize its contents to plan lecture courses or supplement their classes, tailoring the material to suit their teaching objectives.

Dimension: 235 x 155 (mm)
ISBN-13: 9783030871734
Edition number: 1st ed. 2021