The aim of Problems and Solutions for Undergraduate Real Analysis I, as the name reveals, is to assist undergraduate students or first-year students who study mathematics in learning their first rigorous real analysis course. The wide variety of problems, which are of varying difficulty, include the following topics:
- Elementary Set Algebra
- The Real Number System
- Countable and Uncountable Sets
- Elementary Topology on Metric Spaces
- Sequences in Metric Spaces
- Series of Numbers
- Limits and Continuity of Functions
- Differentiation
- the Riemann-Stieltjes Integral
Furthermore, the main features of this book are listed as follows:
- The book contains 230 problems, which cover the topics mentioned above, with detailed and complete solutions. As a matter of fact, my solutions show every detail, every step and every theorem that I applied.
- Each chapter starts with a brief and concise note of introducing the notations, terminologies, basic mathematical concepts or important/famous/frequently used theorems (without proofs) relevant to the topic.
- Three levels of difficulty have been assigned to problems so that you can sharpen your mathematics step-by-step.
- Different colors are used frequently in order to highlight or explain problems, examples, remarks, main points/formulas involved, or show the steps of manipulation in some complicated proofs. (ebook only)
- An appendix about mathematical logic is included. It tells students what concepts of logic (e.g. techniques of proofs) are necessary in advanced mathematics.