In this course we will look at the axiomatic method --- the cornerstone of modern mathematics --- through the historical development of several important mathematical topics. In particular, we will discuss the following topics: The development of geometry concentrating mostly on Euclidian axioms; Numbers, including the Peano axioms for natural numbers, integers and the fundamental theorem of arithmetic, rational numbers as an example of a field, and the long history to the rigorous notion of real numbers; Polynomials as the ``nicest'' functions, including the discovery of complex numbers, fundamental theorem of algebra, and ``infinite'' polynomials, aka power series, that were invented by Isaac Newton; and finally Probability theory, including the axioms of Kolmogoroff, classical probability, and the (basic version of) central limit theorem.

__Classes:__MWF 8:00am-8:50am, NDSU Quentin Burdick Bldg, Room 422__Office hours:__MWF 11:00am-11:50am (Minard 408E32)- Syllabus
__Textbook:__David M. Burton, The History of Mathematics, McGraw-Hill Education; 7 edition (2010) Amazon.

- Week 1. A bird-eye view on the history of mathematics.
- Week 2. The beginning of Greek geometry.
- Week 3. Euclid and the Elements. Euclidian geometry.
- Week 4. Euclidian geometry. Non-Euclidian geometry.
- Week 5. On the way to rigor. Cantor and set theory. Peano's axioms.
- Week 6. Axiomatic development of number sets.
- Week 7. Euclid's number theory. Prime numbers.
- Week 8. Diophantine Equations. Fermat, Euler, and Gauss.
- Week 9. Rational and real numbers.
- Week 10. Spring break.
- Week 11. Solving polynomial equations. Cubic equations and complex numbers.
- Week 12. The fundamental theorem of algebra.
- Week 13. Newton and ``infinite'' polynomials. Birth of calculus.
- Week 14. Axioms of probability theory. Basic combinatorics.
- Week 15. The law of large numbers and the central limit theorem.
- Week 16. Review and additional topics.
- Week 17. Dead week. Presentations.
- Week 18. Final exam (May 13th, Friday, 10:30am). Presentations.

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