Modern Linear Algebra

# MATH - 67

## General Information

Instructor: Indrajit Jana
Meeting: WELLMAN 212; MTWR 12:10-1:50 pm
Textbook: I will follow the textbook "Linear Algebra, As An Introduction to Abstract Mathematics"
Syllabus: The syllabus can be found here.
Important Dates: See the summer session calendar here.
Office Hours: WR 10:00-11:00am or by appointment, in MSB 3125 or 3240

## Homework

There will be proof writing exercises due on every Monday. A sample proof writing exercise and possible mistakes can be found here

## Exams

There will be unannounced quizzes in every week. The material covered in previous lectures/discussions from any day prior (not the material covered on the same day) will be reflected in the quizzes. Quiz problems will be taken mainly from the problem set in the book . I will pick up two or three problems randomly from the problem set and ask you to solve the problem in class (15-20 mins). Sometimes the quiz problem may not be exactly same as the problems in the book but it will be similar to one of those problems. There will not be any midterm. The final exam is scheduled on the last day (September 11, 2014) of the course. Note, there are NO MAKEUP EXAMS!

The grading policy is the following
Proof writing exercises: 20%
Quiz: 30%
Final Exam: 50%
Grading curve will be decided later depending on the class performance.

## SDC

If you need any special arrangement please contact me as early as possible. More precisely, SDC requires me to post the following message.
Any student with a documented disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable accommodations must contact the Student Disability Center (SDC). Faculty are authorized to provide only the accommodations requested by the SDC. If you have any questions, please contact the SDC at (530)752-3184 or sdc@ucdavis.edu.

## Online Resources

There are many software and online resources for viewing/plotting three dimensional surfaces.

## Tentative Lecture schedule and Homework

• $x.y$ indicates the $y$ th proof writing exercise in chapter $x$.
• You do not need to submit the solutions of $*$ marked problems, but you are highly encouraged to do it by yourself as they may appear in quizzes or final exam.
• Homework are due on Mondays (at the beginning of lecture). All exercises given in a week will be collected in the next week. For example, exercises given in the first week will be collected on Monday of the second week.
August 4 What is linear algebra? 1.1
August 5 Complex numbers 2.1, 2.3, 2.4*, 2.5*
August 6 Fundamental theorem of algebra 3.2, 3.3*
August 7 Discussion Quiz 1
August 11 Vector Spaces 4.2*, 4.4
August 12 Span and Bases 5.1*, 5.3, 5.4, 5.6*, 5.7*
August 13 Linear Maps: Defiintion, Null space, Range, Dimension formula 6.5*, 6.7
August 14 Discussion Quiz 2
August 18 Linear Maps: Matrix, Invertibility 6.1, 6.2, 6.4*, 6.8*
August 19 Eigenvalues and Eigenvectors: Invariant subspaces, Eigenvalues, Diagonal matrices. 7.3, 7.4*, 7.6
August 20 Discussion Quiz 3
August 21 Eigenvalues and Eigenvectors: Existence of eigenvalues, Upper triangular matrices. No Homework
August 25 Permutation 7.8, 7.9*, 7.10
August 26 Determinant 8.2, 8.3, 8.4*
August 27 Properties of the determinant No Homework
August 28 Discussion Quiz 4
Sept 1 Holiday; No Class
Sept 2 Inner product Spaces 9.2, 9.4*, 9.5
Sept 3 Orthogonal projections and minimization problems, Change of Bases 9.6, 9.7
Sept 4 Discussion Quiz 5
Sept 8 Self adjoint and normal operators
Sept 9 Spectral Theorem
Sept 10 Review Practice Test
Solutions
Sept 11 Final Exam