How We Got from There to Here: A Story of Real Analysis
Credit: Course image adapted from a figure by Eugene Boman and Robert Rogers and is licensed under CC BY-NC-SA 4.0
Resource Description
The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.
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Credit: Image adapted from figures by Christopher Griffin and is licensed under CC BY-NC-SA 3.0 US
Resource Description
This is a set of lecture notes for Penn State’s undergraduate Linear Programming course.
The lecture notes are (roughly) based on the first 6 chapters of Bazaraa et al.’s Linear Programming and Network Flows book. This is a reasonably good book, written primarily by and for Industrial Engineers. However, it does not present major results in the standard theorem-proof style common to mathematical discourse. This set of notes corrects this situation by presenting the material in a format for presentation to a mathematics class.
Many of the proofs in this set of notes are adapted from the textbook with some minor additions. Additionally, I prefer to present maximization problems, while Linear Programming and Network Flows prefers the minimization format. I’ve modified all the proofs to operate on maximization problems. When used with the book, the student can obtain a complete set of proofs for elementary Linear Programming.
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