Advanced Mathematics: An Invitation in Preparation for Graduate School

Patrick Guidotti

Published by De Gruyter 2022

Advanced Mathematics

An Invitation in Preparation for Graduate School

Patrick Guidotti

In the series De Gruyter Textbook

https://doi.org/10.1515/9783110780925

Overview
Contents

About this book

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.

This reference provides a roadmap for students transitioning from an undergraduate mathematics curriculum and degree into a graduate mathematics curriculum and program.

Author / Editor information

Patrick Guidotti

graduated from the Universität Zürich, did postdoctoral research at the Martin-Luther Universität Halle-Wittenberg and at the California Institute of Technology, where he later held the position of Von Karman Instructor. He is currently a professor at UC Irvine.

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	IX
Foreword Publicly Available Download PDF	XIII
1 Sets and functions Requires Authentication Unlicensed Licensed Download PDF	1
2 Numbers Requires Authentication Unlicensed Licensed Download PDF	7
3 Vectors and their spaces Requires Authentication Unlicensed Licensed Download PDF	28
4 The topology of metric spaces Requires Authentication Unlicensed Licensed Download PDF	49
5 Differentiation Requires Authentication Unlicensed Licensed Download PDF	62
6 Manifolds Requires Authentication Unlicensed Licensed Download PDF	80
7 Ordinary differential equations Requires Authentication Unlicensed Licensed Download PDF	93
8 Optimization Requires Authentication Unlicensed Licensed Download PDF	106
9 Partial differential equations Requires Authentication Unlicensed Licensed Download PDF	127
10 Probability Requires Authentication Unlicensed Licensed Download PDF	150
11 Answers to selected questions Requires Authentication Unlicensed Licensed Download PDF	174
Index Requires Authentication Unlicensed Licensed Download PDF	199

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Seniors and beginning graduate students transitioning to a graduate program in mathematics
Pages
- Front matter: 16
- Main content: 200
Illustrations
- Coloured Illustrations: 30
Keywords: Sets and functions; numbers; vectors; topology; differentiation; manifolds; ordinary differential equations; partial differential equations; probability

eBook

Published: August 1, 2022
ISBN: 9783110780925

Paperback

Published: August 1, 2022
ISBN: 9783110780857