Undergraduate / Masters Math Lectures and Assignments
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Differential Geometry of Manifolds
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Richard G. Klotz, Ph.D.
Adjunct Professor of Mathematics Hunter College
(City University of New York)
This website contains lecture notes and homework assignments for 14 undergraduate and master’s level math courses that I have taught at Hunter College, City College of New York, Columbia University and Stanford University. The courses (listed below) cover most requirements at U.S. colleges/universities for both an undergraduate math major and for non-math majors in other fields. Some may be considered master’s level courses.
The goals of this website are to:
Allow math instructors to teach courses without requiring students to buy a textbook or to supplement their teaching materials.
Provide students with a free resource to supplement any textbook they might be using for a given math course.
All lecture notes and homework assignments are free and may be downloaded. Instructors may download and modify these materials as they choose. Although the lecture notes are intended to cover all relevent aspects of a given math course, the emphasis is on worked examples.
Richard Klotz earned a B.A. in Mathematics at Harvard University and a Ph.D. in Mathematics at Stanford University. Currently an Adjunct Professor of Mathematics at Hunter College, he has also been an Assistant Professor of Mathematics at Columbia University. In 2019, he was awarded the Insdorf Award for Excellence in Teaching.
I would like to thank Professor Barry Cherkas, Chairman of the Mathematics and Statistics Department at Hunter College for his support and assistance in this project. I’m also grateful to Professor Rob Thompson, who brought me to Hunter, and whose help has been invaluable. In addition, I would like to thank April Shenk and Matt Cottell for building this website. Finally, I would like to thank my daughter, Rachel Klotz, who typed and edited the nearly 3,000 pages of lectures note on this site. Her work greatly enhanced the presentation of the material. – Rick Klotz
Choose a course from below:
Calculus 1
Calculus 2
Calculus 3
Vector Analysis
Differential Equations
Linear Algebra
Analysis 1
Analysis 2
Abstract Algebra 1
Complex Analysis 1
Differential Geometry of Curves and Surfaces
Calculus on Manifolds
Differential Geometry of Manifolds
Real Analysis