MATH-223-001 — Spring 2018, TR 2:00pm–3:50pm, Peck Hall 304
Ever since the reformulation of calculus in the middle of the 19th century, mathematicians have been insistent upon maintaining a high standard of rigor. This led to the development of formal logic in the early 20th and using set theory as a foundation of mathematics around the same time.
In this course you will learn the basics of classical logic including propositions, connectives, implications and quantifiers, as well as basic set theory including relations, functions and cardinality. You will also get a brief introduction to combinatorics and graph theory. In addition to the context provided by this material, you will be learning how to read, analyze and write proofs. Believe it or not, proofs are the bread and butter of mathematics whereas almost all your prior coursework has focused on computation. Computation is an important part of mathematics, especially applied mathematics, statistics and cryptography, but it is only a piece the entirety of mathematical thought.
Learning to think logically, read and write proofs requires a rewiring of the way you think, and this is potentially a challenging course for that reason. However, you should commit to devoting serious time to learning the material and how to think like a mathematician because it will pay off in the long run, both in your mathematical studies, and in your future career.
We will use A Transition To Advanced Mathematics, 7th ed., by Douglas Smith, Maurice Eggen, and Richard St. Andre.
At the conclusion of this course, students should be able to:
Time permitting we will cover the construction of the real numbers in terms of Cauchy sequences.
I am maintaining notes on my website, a link to which you can find both at the top of this syllabus and on Blackboard.
You can access them as
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You are expected to read ahead in the book before each class so that you are primed to learn about the material in more depth. I used the word “primed” intentionally: you should think of this reading ahead as being painted with primer so that when you get to class the lecture (i.e., the paint) sticks effectively. The purpose of reading ahead is not to learn everything on your own.
|15 January 2018||Martin Luther King Day, no class|
|19 Janurary 2018||Last day to add/drop with full refund|
|4–11 March 2018||Spring break, no class|
|23 March 2018||Last day to withdraw without permission for
If an emergency arises which requires you to miss an exam, I must be made aware at least two hours prior to the start time of your exam. Note: proper documentation will be required before a makeup arrangement is considered.
Academic misconduct includes, but is not limited to, cheating, plagiarism and forgery, and soliciting, aiding, abetting, concealing, or attempting such acts. Plagiarism may consist of copying, paraphrasing, or otherwise using written or oral work of another without proper acknowledgment of the source or presenting oral or written material prepared by another as ones own. At minimum, cheating will result in that assignment receiving a grade of zero.
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This syllabus is subject to change by the instructor if deemed necessary for the benefit of student learning or to correct errors and omissions.