Honors Linear Algebra and Real Analysis II, Spring 2017

Course Information

Our goal in this class is to study the geometry of functions of several variables, broadly referred to as mathematical analysis. We will construct theories of differentiation and integration and give rigorous proofs of analogues of the classical theorems of calculus in this broader setting. Our main source will be Spivak's Calculus on Manifolds, though lectures will also draw from other similar texts, listed below.

There will be three forms of graded work:

(20% of total) Weekly homework assignments, to be typed up in LaTeX and turned in at the CA's mailboxes (on the second floor of the Science Center) before class each Wednesday. (Expect to spend roughly 12-15 hours a week on this.)
(40% of total) Two midterm exams, dates listed below.
(40% of total) The final exam, date listed below.

Collaboration on homeworks with your peers is highly encouraged! However, you must give citations and indicate what you collaborated on and with whom. (Part of academic gracefulness is being very generous about crediting other people with their ideas.) If you use other resources for help, you should understand what you've read well enough that you could withstand interrogation about it—merely copying an answer is not enough to learn. Finally, collaboration on exams is of course prohibited and will result in academic discipline, which could mean failing the exam, failing the class, or expulsion.

Our general policy about late work is strict: we will not permit assignments to be handed in late or exams to be taken on other days without some written mandate from a doctor or the university administration.

Our meeting times for lecture, for office hours, and with the CAs have all been posted below. I will be updating this webpage throughout the semester.

Contact information

Eric Peterson (Lecturer) (email)
Thayer Anderson (CA) (email)
Davis Lazowski (CA) (email)
Handong Park (CA) (email)
Rohil Prasad (CA) (email)
Benjamin Gunby (GCA) (email)

Schedule, Dates and Times

I have listed below some events (along with dates and times) relevant to the course. In addition to the office hours listed, I am also available by email and by appointment; I have a calendar at this address to facilitate setting up meetings.

Regular class times

Lecture:
- Monday, 10:00am - 11:00am in Sever 213
- Wednesday, 10:00am - 11:00am in Sever 213
- Friday, 10:00am - 11:00am in Sever 213
Supplementary:
- Collaborative homework session: Each Monday, 8:00pm onward in Leverett Dining Hall
- Review session with Benjamin Gunby: Friday, 11:00am - 12:00pm in SC 314

Office hours

Eric Peterson:
- Monday, 11:00am - 12:30pm in SC 229
- Wednesday, 12:30pm - 2:00pm in SC 321h
Thayer Anderson:
- Monday, 8:00pm - (at least) in Leverett dining hall
- Sunday, 8:00pm - 9:00pm in Lowell dining hall
Davis Lazowski:
- Tuesday, 4:00pm - 5:00pm in SC 105
Handong Park:
- Thursday, 4:15pm - 5:30pm in SC 104
Rohil Prasad:
- Monday, 8:00pm - 9:00pm (at least) in Leverett dining hall
Benjamin Gunby:
- Thursday, 3:00pm - 4:00pm in SC 104

Important dates

Drop deadline: Monday, February 6th
Midterm exam: Monday, February 27th, 10:00am - 11:00am in Sever 213
Midterm exam: Friday, March 31st, 10:00am - 11:00am in Sever 213
Final exam: Thursday, May 4th, 9:00am - 12:00pm in SC Lecture Hall E

Homework

Due April 26th:	problem sheet	(solutions)
Due April 19th:	problem sheet	(solutions)
Due April 12th:	problem sheet	(solutions)
Due March 22nd:	problem sheet	(solutions)
Due March 8th:	problem sheet	(solutions)
Due February 22nd:	problem sheet	(solutions)
Due February 15th:	problem sheet	(solutions)
Due February 8th:	problem sheet	(solutions)

Course Materials

Practice final #1 from April 28th.
Practice final #2 from April 28th.
Notes package.
(4.2) Differentiation and k-forms from April 5th.
(4.1) The alternating algebra from April 3rd.
Midterm #2 solutions from March 31st.
Notes from Benjamin Gunby's section from March 24th.
Notes from Benjamin Gunby's Section from March 10th.
Change of coordinates Mathematica demo from March 8th.
Midterm #1 solutions from February 27th.
Notes from Benjamin Gunby's Section from February 24th.
Derivative of matrix inversion from February 22nd.
Notes from Benjamin Gunby's Section from February 17th.
Example of local coordinates from February 15th.
(1.2) More topology on R (Notes by Rohil Prasad) from January 27th.
LaTeX template.
Spivak's Calculus on Manifolds.
Rudin's Principles of Mathematical Analysis.
Hubbard and Hubbard's Vector Calculus, Linear Algebra, and Differential Forms.
Spivak's Calculus.
Madsen and Tornehave's From Calculus to Cohomology.

This is a work in progress.