# 22659 Applied Linear Algebra

Term: Spring 2021 | Units: 4 | Section: 01 | Students enrolled: 40 | Lectures: Sun, Tue 8:00–10:00am | Exam Date/Time: 7/4/21 9:00am | Prerequisite: Linear Algebra I

## Instructor

Mojtaba Tefagh, Math 205, mtefagh@sharif.edu.

Teaching assistants

• Aida Afshar

• Kiana Asgari

• Mobina Azimi

• Nahid Sarem Sangari

## Catalog description

Introduction to applied linear algebra with a focus on applications. Vectors, distance, and angle; applications to clustering (the k-means algorithm) and document analysis. Matrices, left and right inverses, QR factorization; applications to population and epidemic dynamics. Least-squares, constrained and nonlinear least-squares; applications to model fitting, regularization and cross-validation. Additional applications include but are not limited to time-series prediction, tomography, optimal control, and portfolio optimization.

## Prerequisites

Exposure to computer programming and good knowledge of linear algebra (as in 22255 or equivalent background) is a prerequisite or corequisite.
You will use the relatively new Julia programming language to write very simple scripts for computations with vectors and matrices, so basic familiarity with elementary programming will be required. However, a strong background in programming (with Julia or otherwise) is not expected.

## Textbook and optional references

This course is originally developed by Stephen P. Boyd. The course materials are largely the same as that for ENGR108 at Stanford. Specifically, the textbook and lecture slides can be found here.

1. Requirements:

1. Attendance and participation at sections.

2. Biweekly homework assignments, due on Saturdays by 11:59 pm, starting the second week of class. You are allowed, even encouraged, to work on the homework in small groups, but you must write up your own homework to hand in.

3. Theory quiz. The format is a closed book, closed notes midterm, scheduled for the last week of classes before the Nowruz holiday break.

4. Applied quiz. The format is a closed book, closed notes midterm, scheduled for about one month after the Nowruz holiday break.

5. Final exam. The format is an in-class, 120-minute exam, scheduled for Sunday July 4th 9:00 am.

2. Grading: Homework 35%, theory quiz 20%, applied quiz 20%, final exam 25%. These weights ($$\tilde{x}$$) are approximate; we reserve the right to change them later.

1. Update. The final weights are the solution of the following linear program

$\begin{array}{ll} \mbox{maximize} & c^Tx + c_{ExtraCreditProject} + \alpha(1-a)\\ \mbox{subject to} & 1^Tx = 1^T\tilde{x} \\ & \dfrac{1}{a} \leq \dfrac{x_i}{\tilde{x}_i} \leq a, \quad 1\leq i\leq 4, \end{array}$

where $$c_1$$, $$c_2$$, $$c_3$$, and $$c_4$$ are the normalized homework, theory quiz, applied quiz, and final exam grades, respectively.

## Homework grace period

You are given 9 “grace days” (counted in 24-hour periods) if you need extra time because of a serious problem, use them wisely! The cutoff for on-time submission is 11:59:00 pm on the due date, and submitting at 11:59:01 pm is the same as 11:59:00 pm the next day. Late submissions will not be accepted after the hard deadline of 48 hours past the original due date.