Math 32300, Section LM, Fall 2018:
Advanced Calculus I
- The course textbook is freely (and legally) available from Springer while you are on campus.
These are all pdf documents. Some documents are password protected. The password is always the same and was provided in class and over email.
||TuTh 10-11:40am in NAC 6/121
||Prof. Pat Hooper
Tuesdays 12-1pm and Thursdays 5-6pm on any day our class meets. Appointments are accepted.
- Some textbooks you might consider looking at related to the topics of the book:
- Introduction to Real Analysis, by Trench. (At the level of the course. Freely available.)
- Principles of Real Analysis, by Rudin. (A more advanced book.)
- Real Mathematical Analysis, by Pugh. (A slightly more advanced book, but a creative and interesting book.)
- Mohammad Reza Pakzad "Introduction to Theoretical Math" course page:
This page course has a supplement on Logic and Proof covering logic, quantifiers, and some proof techniques. (This covers material pre-requisite to this course.)
- Lecture notes from an open course at MIT on "Mathematics for Computer Science"
These notes may be useful for reviewing basic logic and logical proofs, including statements involving quantifiers. (See lectures 1 and 2.) This link was included for the same reason as the link above. (This covers material pre-requisite to this course.)
Euler-Maclaurin Summation Formula:
This page proves the following Theorem. (See the very bottom of the page.)
Theorem. Suppose f is continuous, positive, and decreasing on the interval [1,∞). Then, the series Σn=1∞ f(n) and the integral ∫1∞ f(x) dx either both converge or both diverge.
Visit Prof. Hooper's website