MATH
174-Spring 2022
Instructor: Alex Iosevich
Office: Hylan 909
email: iosevich@math.rochester.edu
Office Hours: 1-2 p.m. MW and by appointment
Textbook: Calculus on manifolds, by Spivak
Grading: Homework (%20), In-class midterm (%25), Take-home
project (%20), and Final (%35).
Structure of the class:
This is going to be a highly interactive class. I expect frequent
in-class discussions designed to make sure that the material is
absorbed in real time. Notes will be prepared and distributed ahead
of time.
Structure of the exams and the final:
The exams are designed to test both the knowledge of the proofs and
the ability to apply the theoretical results in concrete instances.
Expectations:
The students will be expected to come to each class prepared. What
this means is that on any given day, I expect the students to know
and understand the proofs and examples that were covered
in class up to that point. In addition, the students will be
expected to read ahead and anticipate the material that is going to
be covered.
Homework #1: due Sunday, January 29, 11:59 p.m.
Page 4: 1,2,5,6,7,8,10,12,13
Page 10: 15,16,19,21
Page 13: 24,25,27,29,30
Homework # 2: due Sunday, January 5, 11:59 p.m.
Pages 17-18: problems 1, 2, 8
Pages 22-23: problems 10, 12, 16
Pages 27-28: problems 17, 21, 22, 23, 25, 26
Homework # 3: due Tuesday, February 21, 11:59 p.m.
Pages 33-34: problems 28, 29, 32, 34, 35
Pages 39-40: problems 36, 37
Pages 49-50: problems 1,2, 5, 6, 7
Homework # 4: due Tuesday, February 28, 11:59 p.m.
Page 52, problems 9, 11, 12
Page 56, problems 15, 18, 20
Page 61: problems 25, 27, 28, 32, 34
Homework # 5: Due Tuesday, March 28, 11:59 p.m.
Page 84, problems 1, 2, 3, 4, 9, 10
Page 96, problems 13, 14, 16, 18, 21
Homework # 6: Due Wednesday, April 28, 11:59 p.m.
Page 100, problem 23
Page 104-108, problems 25, 29
Page 114-115, problems 1,5
Page 125-126, problem 20
Page 130, problem 23, 26
Lectures
Chapter 1: January 18, 2023
Lectures
Chapter 2: February 5, 2023
Lectures Chapter
3: February 27, 2023
Lectures
Chapter 4: April 9, 2023