``If it be then your Pleasure, ye Lovers of Study, come always; be not restrained through any Fear, nor retarded by too much Modesty, what you may do by your Right, you shall make me do willingly, nay gladly and joyfully. Ask your Questions, make your Enquiries, bid and command; you shall neither find me averse nor refractory to your Commands, but officious and obedient. If you meet with any Obstacles or Difficulties, or are retarded with any Doubts while you are walking in the cumbersome Road of this Study of Mathematics, I beg you to impart them, and I shall endeavour to remove every Hindrance out of your Way to the best of my Knowledge and Ability.''
Isaac Barrow, March 14, 1664
What is it about mathematics that makes it so powerful, so insightful? How can it claim the absolute and universal truths that are denied even to science? Why is it that the patterns that mathematicians treasure purely for their aesthetic beauty are the ones that are so useful for understanding the world in which we live?
This will be a free-ranging course that explores the world of mathematics by doing mathematics and by exploring the works of those who have thought about these questions.
The mathematics we do will be problems, techniques, and theory of discrete mathematics including combinatorics and number theory. Examples include:
We will take excursions into the modern history of discrete mathematics including unsolved problems and current research in issues such as factorization, primality testing, and public key encryption (RSA). The emphasis will be on problem-solving, both individually and in groups.
We also will read and discuss what two of the great thinkers of the twentieth century, G. H. Hardy and Imre Lakatos, have had to say about the nature of mathematics.
There are no prerequisites for this course except for a willingness to work hard at exploring the world of mathematics.
All assignments for this course and reminders of what is coming due are on the course website at www.macalester.edu/~bressoud/courses/sched136.html.
Answers can be very brief. Five points are available for advance reading. If you submit answers for at least 25 of the readings, you will earn all five points. 20–24 earns four points. 15–19 earns three points. 10–14 earns two points. 5–9 earns one point. Less than 5 earns no points.
Grades will be assigned on a straight 90% = A, 80% = B, 70% = C, 60% = D, although I reserve leeway in the assignment of + and -.
I encourage you to work with your classmates on homework assignments, problem sets, and projects. You may not discuss or share information about the examinations until all students have turned them in. Please be careful about what you leave where others could see it. Evidence of using someone else's work as your own will be processed according to the procedures outlined in the Student Handbook.
The preceptor for this class is Kate Herbig. Her email is kherbig@macalester.edu. Her phone number is 7675. She'll be holdinng study sessions on Sunday afternoons at 2:00 pm. Meet in the Math/Comp Sci Reading Room, 254 Olin Rice. (When you come in the main door, go to the second corridor on your left. The Reading Room is the second room on your right down this corridor, just before the Math/CS computer labs.)
S. C. Coutinho, The Mathematics of Ciphers: Number Theory and RSA Cryptography, A K Peters
G. H. Hardy, A Mathematician's Apology, Cambridge University Press
Imre Lakatos, Proofs and Refutations: The Logic of Mathematical Discovery, Cambridge University Press
Andrea A. Lunsford, Easy Writer, 2nd ed., Bedford/St. Martin's
Daniel A. Marcus, Combinatorics: A Problem Oriented Approach, Mathematical Association of America