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Math Studies, Course Lecture Notes, Academic Year 2009-2010, by Walter Noll

This website was created to publish some work created since about 1970 for use in an undergraduate honors program called Mathematical Studies. The purpose of this program has been to present mathematics as an integrated whole, and to avoid its traditional division into separate and seemingly unrelated courses. We hope that someone elsewhere in the world may agree with our approach and use some or all of the work published here. If so, we would appreciate being informed.

Publications by Walter Noll

A. General

1) Math Studies, Course Description
2) The Origin of Math Studies at CMU
3) The Conceptual Infrastructure of Mathematics
4) What is Mathematics all about?
5) The Role of the Professor
6) Mathematics Should not be Boring

B. Technical

1) Summary of Elementary Calculus
2) Limits and Continuity
3) Differentiation
4) Integration
5) Sequences of Functions
6) The Gamma Function
7) Monoids
8) Groups
9) Rings

C. Finite-Dimensional Spaces, Algebra, Geometry, and Analysis

1) Basic Mathematics
2) Linear Spaces
3) Duality, Bilinearity
4) Flat Spaces
5) Inner Product Spaces
6) Topology
7) Differential Calculus
8) Volume Integrals
9) Coordinate Systems