Marvin J. Greenberg & John R. Harper 
Algebraic Topology [PDF ebook] 
A First Course

A web map is an interactive display of geographic information, in the form of a web page, that you can use to tell stories and answer questions. Web maps have numerous advantages over traditional map …

This book presents the fundamentals of the shock wave theory. The first part of the book, Chapters 1 through 5, covers the basic elements of the shock wave theory by analyzing the scalar conservation …

Ultrafilters and ultraproducts provide a useful generalization of the ordinary limit processes which have applications to many areas of mathematics. Typically, this topic is presented to students in …

Introduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common di …

This work addresses all of the major topics in Fourier series, emphasizing the concept of approximate identities and presenting applications, particularly in time series analysis. It stresses through …

Data Analytics: A Small Data Approach is suitable for an introductory data analytics course to help students understand some main statistical learning models. It has many small datasets to guide stud …

Applied topology is a modern subject which emerged in recent years at a crossroads of many methods, all of them topological in nature, which were used in a wide variety of applications in classical m …

This book develops a mathematical theory for finance, based on a simple and intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial liability, start …

The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. T …

This book illuminates the complex process of problem solving, including formulating the problem, collecting and analyzing data, and presenting the conclusions. …