We will not be using a traditional textbook this semester, but rather a problem sequence adopted for an inquiry-based learning (IBL) approach to real analysis. The problem sequence that we are using is an adaptation of the analysis notes by Karl-Dieter Crisman, which are a modified version of notes by W. Ted Mahavier. Both authors have been gracious enough to grant me access to the source of these notes, so that we can modify and tweak for our needs if necessary. The notes will be released incrementally. Each link below is to a PDF file.
Introduction to Real Analysis (complete set of notes)
I will not be covering every detail of the notes and the only way to achieve a sufficient understanding of the material is to be digesting the reading in a meaningful way. You should be seeking clarification about the content of the notes whenever necessary by asking questions. Here’s one of my favorite quotes about reading mathematics.
Don’t just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?
Below are links to the take-home portions of each exam. If you are interested in using LaTeX to type up your solutions, contact me and I will send you a link to the source file of the exam.
Mathematics & Teaching
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MAT 226: Discrete Math
MAT 320: Foundations
MAT 431: Analysis
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