A mathematician, like a painter or a poet, is a maker of patterns.  If his patterns are more permanent than theirs, it is because they are made with ideas… The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way.  Beauty is the first test: there is no permanent place in the world for ugly mathematics… The ‘seriousness’ of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. – G. H. Hardy

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigor should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.  -W.S. Anglin

In this class you will transform from consumers of mathematics to creators; learning to use the tools of conjecture, abstraction, and logic to construct mathematical proofs. Proof writing is an integral part of all upper-level mathematics courses, and the method by which mathematicians extend the boundaries of what is known.  It takes persistence, creativity, clarity, logical thinking, and an ability to see connections and patterns - skills which will help you in whatever field you pursue.  Through this course you will: learn to read, understand, and compose mathematical proofs; distinguish valid arguments from invalid ones; formulate, write, and present logical arguments; develop your aesthetic sense in mathematics; and strengthen your analytic reasoning skills.

Tentative Schedule: 

Syllabus: 

http://willamette.edu/~emcnicho/courses/Syllabi/SyllabusMath251WFoundationsS17.pdf