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What's new!
o I will be away for the first week. Prof. Jiang will substitute me for this week. o No class on Friday September 4. o See below for course info and the text book. o Sep. 9: reviewed basic concepts of vector space over a field, linear dependence, spanning set, basis, direct (Cartesian) sum of vector spaces. o Sep. 9: First homework will be posted today. It is due next week on Friday. o Sep. 11: Problem 3 in HW1 had a careless mistake. It is fixed now. o Sep. 16: We finished Chapters 2 (duality), except for the last theorem (Theorem 7) about quadrature formula which will be discussed on Friday. o Sep. 18: HW2 is now posted. o Sep. 26: We are finished with dual or transpose of a linear mapping. Next time we will discuss similar matrices and projections. o Sep. 26: HW3 is now posted. o Oct. 2: HW4 is posted. o Oct 2: We discussed the notion of a group acting linearly on a vector space (also called a representation). We explained the averaging operator (when G is a finite group). We left it as an exercise that this is an example of a projection. o Midterm 1 is on October 15th (Thursday, same time and location as the recitation). o Midterm 1 covers all the material discussed in class from Chapter 1 to 4 (inclusive). o There will be 5 problems, one of which is to state definitions/theorems. o Problems are similar to exercises in the text book and homework problems. o Note that we changed midterm time to Thursday (same time and location as recitation)! o HW5 is now posted. It is due next Friday. o HW6 is posted and due next Friday October 30th. o Oct. 31: HW7 is posted and due next Friday November 6. o Oct. 31: We are covering eigenvalues and eigenvectors. Next time we will finish the proof of Spectral Theorem which states that there is a basis consisting of generalized eigenvectors. o Oct. 31: The second midterm will be on Friday November 20th during the class. It focuses on material covered after the first midterm. o Nov. 2: Solutions to MT1 posted. o Nov. 8: HW 8 posted. It is due on Monday Nov. 16. o Nov. 15: Midterm 2 info posted. o Nov. 15: I also posted some extra problems from last years homeworks. Problems in the midterm are not necessarily same level of difficulty (probably easier). o Nov. 15: It is also useful to look at previous years linear algebra prelim problems (related to the topics covered so far). These can be found at: Previous prelim exams o Nov. 22: HW 9 posted. o Nov. 23: Solutions to Midterm 2 posted. o Nov. 23: We covered orthogonal matrices and matrix norms. o Dec. 5: HW10 is posted. It is due next Friday. o Dec. 6: The last homework due date extended to Monday Dec. 14th. o The final exam is during the last class (Friday Dec. 18). Same time and location as the lectures. It is 2 hours long. o Dec. 13: Here are notes from last year. These cover material for two course MATH2370 and MATH2371. We did not cover all the material in these notes. I am posting them here just for extra reference. o Dec. 13: I posted final exam info sheet below. o Dec. 13: I have also posted some practice problems for final as well. Some of them are from previous prelim exams, and some other ones are just for practice or review. Weekly homework o Homework 1 o Homework 2 o Homework 3 o Homework 4 o Homework 5 o Homework 6 o Homework 7 o Homework 8 o Homework 9 o Homework 10 o Solutions to midterm 1 o Midterm 2 info o Extra problems from previous years homeworks o Solutions to midterm 2 o Final exam info sheet o Some practice problems Course Information Course description: Linear transformations of finite dimensional vector spaces are studied in a semi-abstract setting. The emphasis is on topics and techniques which can be applied to other areas, e.g. bases and dimension, matrix representation, linear functionals, duality, canonical forms, vector space decomposition, inner products and spectral theory. Text: The course is based on Lax’s “Linear algebra and applications”. Time of lectures: Monday-Wednesday-Friday 10:00AM - 10:50AM Location of lectures: 524 Thackeray Hall o There will be midterms and weekly homeworks. o Homework is assigned each Friday and is due the next Friday in class. I will announce when the first homework is posted. o Final grade is 50% final exam, 25% midterms and 25% homeworks (lowest hoemwork will be dropped). o Important dates: Aug. 31: first class Sep. 7: Labor Day (no class) Oct. 19: Fall Break (no class) Nov. 25 - 29: Thanksgiving recess (no class) Dec. 11: last class Oct. 15: First midterm Nov. 20: Second midterm Dec. 18: Final exam (same time and location as the lectures) Instructor's Information Email: kavehk AT pitt.edu Office: Thackeray #424 Office hours: 11:00AM-12:00PM Tuesdays or by appointment. You can drop by I am usually in. Office phone: 412-624-8331 |