Advanced Mathematics : : An Invitation in Preparation for Graduate School / / Patrick Guidotti.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1
• VerfasserIn: Guidotti, Patrick,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2022]; ©2022
• Year of Publication: 2022
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (XVI, 200 p.)

This exploration of a selection of fundamental topics and general purpose tools provides a roadmap to undergraduate students who yearn for a deeper dive into many of the concepts and ideas they have been encountering in their classes whether their motivation is pure curiosity or preparation for graduate studies. The topics intersect a wide range of areas encompassing both pure and applied mathematics. The emphasis and style of the book are motivated by the goal of developing self-reliance and independent mathematical thought. Mathematics requires both intuition and common sense as well as rigorous, formal argumentation. This book attempts to showcase both, simultaneously encouraging readers to develop their own insights and understanding and the adoption of proof writing skills. The most satisfying proofs/arguments are fully rigorous and completely intuitive at the same time.

Table of Contents

Frontmatter -- Contents -- Foreword -- 1 Sets and functions -- 2 Numbers -- 3 Vectors and their spaces -- 4 The topology of metric spaces -- 5 Differentiation -- 6 Manifolds -- 7 Ordinary differential equations -- 8 Optimization -- 9 Partial differential equations -- 10 Probability -- 11 Answers to selected questions -- Index