## Overview

This course covers basic concepts of linear algebra, with an emphasis on computational techniques. Linear algebra plays a fundamental role in a wide range of applications from physical and social sciences, statistics, engineering, finance, computer graphics, big data and machine learning. We will study vectors, vector spaces, linear transformations, matrix-vector manipulations, solving linear systems, least squares problems, and eigenvalue problems. Matrix decompositions (e.g. LU, QR, SVD, etc.) play a fundamental role in the course.

## 2: 01 In-Class Assignment - Welcome to Matrix Algebra with computational applications

Alexander Paulin

[email protected]

Linear Algebra and Differential Equations 54 (002 LEC) Spring 2018

**Lectures:** MWF, 11am-12pm, Wheeler Hall Auditorium. **Office hours :** MWF 2pm-4pm, TT 3pm-5pm, 796 Evans Hall. **Discussion sections:** Three, one hour sessions each week on MWF. Here is a link with further details. You may only attend the discussion section for which you are enrolled. Here is a link to GSI office hours. You may attend any office hour your please.

**(1/12)**

Welcome to Math 54! This fantastic course is an introduction to linear algebra and its applications to differential equations. At first glance linear algebra is just about solving systems of linear equations. However, after digging a little deeper, we'll discover a rich new language which will be applicable across all mathematical disciplines. This is something of a watershed course, opening up a whole branch of mathematics. It's going to be great!

**(1/12)**

Everything related to the course will be on this website. We will not be using bCourses. There will be weekly homework (posted below) which will be due every Friday in discussion section. In addition to this there will be weekly quizzes. I have office hours everyday of the week so there should always be an opportunity to get my help if you need it. If you can't make any office hours, e-mail me and we'll find another time to meet. In addition to this I will be posting my own lecture notes on this website at the end of each week. You'll be able to link to them directly from the detailed syllabus below. There will also be video recordings of the lectures posted at the end of Monday, Wednesday and Friday. Again you'll be able to link to them directly from the syllabus below.

**(1/12)**

Discussion sections will begin on Wednesday the 17th of January.

**(1/12)**

Make sure to read the course policy and the detailed syllabus below.

**(1/12)**

The first homework assignment will be due on Friday of week 2. The first quiz will also be on Friday of week 2.

**Linear Algebra and Differential Equations (UC Berkeley Custom Edition), 3rd Edition, ISBN: 9781323720868.**

This is a combination of two separate textbooks. These textbooks are

**Linear Algebra and its Applications, Lay-Lay-Macdonald, 5th Edition.**

**Fundamentals of Differential Equations, Nagle-Saff-Snider, 9th Edition**

I strongly advise you against buying these textbooks individually. They contain far more material than will be needed and will be substantially more expensive. We've negotiated a reduced price for the custom textbook if you buy it directly from the publisher. Here's the link:

Pearson Textbook Website Enter Username: algebra and Password: berkeley

You can also buy this textbook from the Cal Student Store for $95 new.

Homework assignments are due each Thursday in section. They will be posted here along with solutions and videos of me going through a selection of the more challenging problems. Your two lowest homework scores will be dropped. The homework corresponding to material covered during a given week is due in the following week's Thursday discussion session.

Assignments will be graded on a coarse scale based on spot checks for correctness and completeness. Your two lowest scores will be dropped. You may discuss the homework problems with your classmates, but **you must write your solutions on your own.** Doing the work yourself is crucial to learning the material properly. Make use of discussion sections, office hours, study groups, etc. if you need assistance, but in the end, you should still write up your own solutions.

I am aware that it is not hard to find solutions manuals on the internet. Copying said solutions on a homework assignment is illegal and will result in a negative grade for that assignment, and potentially in more serious consequences. (Also, it will not help you learn the material).

The homework load for this course is heavy at times, but it is essential for learning the material. Be organized, and don't leave things for the last moment. (You cannot complete the homework assignment if you start on the night before it is due.) Work in small installments, and ask questions in section and during office hours.

Quizzes will take place roughly every week in the Friday discussion section. They will last about 15 minutes, be of closely related to the homework problems for that week. Your two lowest scores will be dropped from your grade. Here is the quiz schedule:

For more detailed information see the course policy

There will be two midterms and a final. There will be no make-up exams, unless there are truly exceptional circumstances. Because of the grading scheme, you can miss one midterm, for whatever reason, without penalty. On the other hand, missing both midterms or missing the final will seriously harm your grade and make it very difficult/impossible to pass the course. Please check the dates now to make sure that you have no unavoidable conflicts!

**First midterm: February 12 in class****Second midterm: March 23 in class****Final exam: May 8 (7pm-10pm)**

Calculators and notes will NOT be allowed for the exams.

To obtain full credit for an exam question, you must obtain the correct answer and give a correct and readable derivation or justification of the answer. Unjustified correct answers will be regarded very suspiciously and will receive little or no credit. The graders are looking for demonstration that you understand the material. To maximize credit, cross out incorrect work. We will be scanning all exams so you will get them back electronically.

After each midterm, there will be a brief window when you can request a regrade. In general, midterm exam grades cannot be changed. The only exception to this is then there has been a clerical error such as a mistake in adding the scores (if this is the case immediately inform your GSI) or if part of the solution has been accidentally overlooked by the grader. Regrade requests may result in a lowering of your grade. As per university policy, final exams cannot be regraded.

**DSP students** requiring accommodations for exams must submit to the instructor a "letter of accommodation" from the Disabled Students Program *at least two weeks in advance*. Due to delays in processing, you are encouraged to contact the DSP office before the start of the semester.

**Cheating** is unacceptable. Any student caught cheating will be reported to higher authorities for disciplinary action.

There will be two midterms, the first on **Monday February 12** and the second on **Friday March 23** . The final exam will be on **Monday May 7 (7pm - 10pm)**.

For more detailed information see the course policy

Grades are calculated as follows:

Each midterm and final score will first be curved into a number on a consistent scale. More precisely, I will assign a number to each exam (midterm 1, midterm 2 and the final) reflecting their relative position in the class. As an example, if you scored 70/120 on the first midterm and exactly 60 percent of the class got this score or below, you'd be assigned the scaled score of 60/100 for that midterm. These numbers are just a reflection of your relative performance. They do not correspond to letter grades in the usual sense. Section scores will be adjusted to account for differences between GSI's in quiz difficulty and grading standards. **Your lowest scaled midterm score will be replaced by the scaled final exam score if it is higher.** Finally, the scaled scores will be added up (with proportions outlined above) giving a final course score between 0 and 100. This score gives an extremely accurate description of your overall relative performance.

This is not high school. For example, you do not need to get 90 or above to get an A. Your final letter grade will ultimately be decided by your ability to demonstrate a crisp understanding of the material and the ability to apply it to a diverse set of problems. Broadly speaking I will be looking for the following criteria for each letter grade:

- A-/A/A+: A clear demonstration that the central concepts have been fully understood Computational techniques (and their many subtleties) have been mastered and can be applied accurately to a diverse problem set A strong understanding of how the abstract concepts can be applied to many real world applications.
- B-/B/B+: Demonstration that the central concepts have been reasonably understood, but perhaps with minor misunderstandings Core computational techniques have been reaonably understood (but generally not key subtleties) and can be applied fairly accurately to a fairly large problem set Reasonable understanding of how the abstract concepts can be applied to some real world applications.
- C-/C/C+: Demonstration that the central concepts have been vaguely understood, but with major misunderstandings Core computational techniques have been poorly understood and can be a applied accurately only in the most standard examples Weak understanding of how the abstract concepts can be applied to even basic real world applications.

To be as fair as possible, I will also take into account the historic average of the class. This means that if I set an exam which is too difficult it will be taken into account in the final letter grades.

**Please note:** incomplete grades, according to university policy, can be given only if *unanticipated events beyond your control* (e.g. a medical emergency) make it impossible for you to complete the course, *and if you are otherwise passing* (with a C- or above).

**Enrollment:** For question about enrollment contact Jennifer Pinney.

The Student Learning Center provides support for this class, including full adjunct courses, review sessions for exams, and drop-in tutoring. This is a truly fantastic resource. I definitely recommend you take advantage of it.

Lecture Notes Chapter 6.2

## Applied Linear Algebra

**Office**: MSB 202 ** Phone**: (860) 486 9153

**: T, Th 11:00-12:00 and by appointment .**

Office Hours

Office Hours

Open Door Policy: You are welcome to drop by to discuss any aspect of the course, anytime, on the days I am on campus-- Tuesdays and Thursdays.

Section 001: Tuesday, Thursday 12:30-1:45. Classroom MSB 403

Section 005: Tuesday, Thursday 2:00-3:15. Classroom MSB 311

Linear Algebra and its Applications, by David C. Lay, 4th edition

This course provides an introduction to the concepts and techniques of Linear Algebra. This includes the study of matrices and their relation to linear equations, linear transformations, vector spaces, eigenvalues and eigenvectors, and orthogonality.

Homework will be assigned after every section, collected on Thursdays, and returned the following class. Solutions to selected homework exercises will be discussed and handed out at that time. For that reason, late homework will not usually be accepted. Homework assignments consist of individual practice exercises from the textbook (see Syllabus below) and occasional group projects. You are encouraged to work with other students in this class on all your homework assignments. Group projects, one report per group, will be graded for exam points. Textbook homework assignments, handed in individually, will not be graded, but will carry exam points (this will be explained in more details in class).

You will need to show your work on exams and homework assignments, but may use calculators, in all cases, to double check your answers and save time on routine calculations. The recommended graphic Calculator is TI83 (best value for the money) but others will do as well.

**Exam Schedule and Guidelines **

There will be two **evening** exams during the semester and a final exam. None is strictly cumulative, but there will be overlap of material between the exams. NO MAKE-UP EXAMS unless there is a very serious emergency for which you provide proof. Quizzes will be given only if necessary. Note: PBB = Pharmacy/Biology Building (It is very close to MSB) PB = Physics Building ( It is on the first floor of MSB).

Exam Schedule Sections 01 and 05 | Exam Guidelines (an active link to each exam guidelines will appear in the week before each exam) |

Exam 1: Thursday, February 20, 6:30-8:30, PBB 129 PBB = Pharmacy and Biology Building | Exam 1 Guidelines: Material and Review Suggestions Attention students: Solutions to homework exercises for sections 1.4, 1.5, 1.7 |

Exam 2: Thursday, April 3, 6:30-8:30, PBB 129 PBB = Pharmacy and Biology Building | Exam 2 Guidelines: Material and Review Suggestions Attention students: Links to solutions to homework exercises can be found in the syllabus below |

Final Exam: Friday, May 9, 1:00-3:00, PB 38 PB = Physics Building | Final Exam Guidelines: Material and Review Suggestions Attention students: Additional office hours: Friday, May 9, 11:00-12:30 |

For help with location of the exam building click on The Campus Map.

UConn Final Exam Policy.

Homework, quizzes, and group projects about 10%. Each Exam (including the Final Exam) is of equal weight, that is, about 30%.

Extra Help: The Q Center and Textbook Website

## 2: 01 In-Class Assignment - Welcome to Matrix Algebra with computational applications

A lot of students get confused while understanding the concept of time-complexity, but in this article, we will explain it with a very simple example:

Imagine a classroom of 100 students in which you gave your pen to one person. Now, you want that pen. Here are some ways to find the pen and what the O order is.**O(n 2 ):** You go and ask the first person of the class, if he has the pen. Also, you ask this person about other 99 people in the classroom if they have that pen and so on,

This is what we call O(n 2 ). **O(n):** Going and asking each student individually is O(N). **O(log n):** Now I divide the class into two groups, then ask: “Is it on the left side, or the right side of the classroom?” Then I take that group and divide it into two and ask again, and so on. Repeat the process till you are left with one student who has your pen. This is what you mean by O(log n).

I might need to do the O(n 2 ) search if only one student knows on which student the pen is hidden. I’d use the O(n) if one student had the pen and only they knew it. I’d use the O(log n) search if all the students knew, but would only tell me if I guessed the right side.

**NOTE :** We are interested in rate of growth of time with respect to the inputs taken during the program execution .

**Another Example:**

Time Complexity of algorithm/code is **not** equal to the actual time required to execute a particular code but the number of times a statement executes. We can prove this by using time command. For example, Write code in C/C++ or any other language to find maximum between N numbers, where N varies from 10, 100, 1000, 10000. And compile that code on Linux based operating system (Fedora or Ubuntu) with below command:

You will get surprising results i.e. for N = 10 you may get 0.5ms time and for N = 10, 000 you may get 0.2 ms time. Also, you will get different timings on the different machine. So, we can say that actual time requires to execute code is machine dependent (whether you are using pentium1 or pentiun5) and also it considers network load if your machine is in LAN/WAN. Even you will not get the same timings on the same machine for the same code, the reason behind that the current network load.

Now, the question arises if time complexity is not the actual time require executing the code then what is it?

**The answer is :** Instead of measuring actual time required in executing each statement in the code, we consider how many times each statement execute.

For example:

## MATH 340L: Matrices and Matrix Calculations

rusin/340L/ It is unlikely that I will post any important material to Blackboard or Canvas for any additional information I want to give you outside of class you should come to this webpage. NEW EDITS

You asked me to write down the homework assignments that I announced in class. I will keep them on a separate page here -->

### Catalogue Description:

- Linear Equations in Linear Algebra,
- Matrix Algebra,
- Determinants,
- Vector Spaces,
- Eigenvalues and Eigenvectors,
- Orthogonality and Least Squares, and
- Symmetric Matrices and Quadratic Forms.

There are two Linear Algebra courses at UT, Math 340L and Math 341, which are fairly similar. You cannot earn UT credit for both of them. Ordinarily, math majors must take Math 341, and no one else may. Math 340L focuses on computation and application Math 341 on theory and proof. Please see an advisor in MPAA (on the ground floor of RLM) if you need assistance enrolling in the appropriate Linear Algebra course.

### Pre-requisites

One semseter of calculus with a grade of at least C- .

### Graded material

Homework: I will assign homework problems, typically taken from the book, approximately weekly. I will use a grader to try to get as much of your responses graded as possible but I strongly encourage you to self-grade, that is, consult with me or your classmates to know that your answers are good. Remember, you do homework primarily to learn the material, not to score points.

I will give a grade for each homework set, then drop the lowest two, then scale your remaining total to a 100-point scale as part of your semester grade.

- due Monday, Aug 31 due Wednesday, Sep 09 due Wednesday, Sep 16 due Friday, Sep 25 due Friday, Oct 02 due Friday, Oct 09 due Friday, Oct 16 due Wednesday, Nov 04 due Wednesday, Nov 11 due Friday, Nov 20 due Friday, Dec 04

Quizzes: I reserve the right to give a few pop quizzes during the semester. Each of these will be treated as another homework assignment (and in particular, for some of you these may be among the two dropped homework assignments).

Exams: There will be 3 mid-term exams, to be held during the usual class period, and a comprehensive final exam. Each midterm is worth 100 points and the final is worth 200 points.

Textbooks, notes, and electronic devices (including phones and calculators) are not permitted during exams. The exams will be a mix of multiple-choice and free-response questions the ratio will change as the semester progresses.

### Letter Grades

No letter grades will be assigned to the midterms or homeworks, but you should keep track of where you stand: I will advise you of the class averages and you can use this information as a rough guideline to where you stand.

### Policies

Classroom activity: Our meeting times together are very short so we must make the most of them. Come to class daily and ask questions this is greatly facilitated by reading ahead each day and doing the homework problems as they are assigned. Please silence your cell phones. I will always assume that any conversations I hear are about the course material so I may ask you to speak up.

Make-ups: it is in general not possible to make up missing quizzes or homework assignments after the due date. If you believe you will have to miss a graded event, please notify me *in advance* I will try to arrange for you to complete the work early.

Students with disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.

Religious holidays: If you are unable to participate in a required class activity (such as an exam) because it conflicts with your religious traditions, please notify me IN ADVANCE and I will make accommodations for you. Typically I will ask you to complete the required work before the religious observance begins.

Academic Integrity. Please read the message about Academic Integrity from the Dean of Students Office. I very much prefer to treat you as professionals whose honesty is beyond question but if my trust is violated I will follow the procedures available to me to see that dishonesty is exposed and punished.

Campus safety: Please familiarize yourself with the Emergency Preparedness instructions provided by the university's Campus Safety and Security office. In the event of severe weather or a security threat, we will immediately suspend class and follow the instructions given. You may wish to sign up with the campus alert programs.

Counseling: Students often encounter non-academic difficulties during the semester, including stresses from family, health issues, and lifestyle choices. I am not trained to help you with these but do encourage you to take advantage of the Counselling and Mental Health Center, Student Services Bldg (SSB), 5th Floor, open M-F 8am-5pm. (512 471 3515, or www.cmhc.utexas.edu

Add dates: If you enroll within the first four class days of the semester, and have missed any graded material, I will adjust the weighting of your graded sections accordingly so that you are not penalized. No such accommodation is made for students who enroll on the 5th day or later. (Such students must enroll through the MPAA advising center in RLM, and ordinarily I do not admit students who ask to enroll then if they have missed any graded activities).

Drop dates: Aug 31 is the last day to drop without approval of the department chair Sept 11 is the last day to drop the course for a possible refund Nov 3 is the last day an undergraduate student may, with the dean's approval, withdraw from the University or drop a class except for urgent and substantiated, nonacademic reasons. For more information about deadlines for adding and dropping the course under different circumstances, please consult the Registrar's web page, http://registrar.utexas.edu/calendars/14-15/

Computers: We don't make use of sophisticated software in this class, but if you find this interesting, you are welcome to use the department's computer facilities. Our 40-seat undergrad computer lab in RLM 7.122, is open to all students enrolled in Math courses. Students can sign up for an individual account themselves in the computer lab using their UT EID. We have most of the mainstream commercial math software: Mathematica, Maple, Matlab, etc., and an assortment of open source programs. If you come to my office you will see me use some of this software to help illustrate concepts. Please see me if you would like more information.

You may find the online row reducer useful for completing computational homeworks. If you have a graphing calculator, you can do it in there as well.

### Schedule

The following table is a tentative schedule for the course. Please be aware that material may be reordered, added or deleted. Pay attention in class --- I'll let you know if we're doing something different.

## Topics in Mathematics with Applications in Finance

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## 2: 01 In-Class Assignment - Welcome to Matrix Algebra with computational applications

• Welcome to CS131!

• Schedule information may change during the quarter please visit the Syllabus page regularly to stay up to date.

• **Lecture location has changed to 370-370 due to the high volume of student enrollment.**

Office: Room 246, Gates Building

Office hours: Tuesday, 3-4pm

Office: Room 243, Gates Building

Office hours: By Appointment

Class forum on Piazza (please ask all questions here if possible): piazza.com/stanford/fall2016/cs131

Additional reference material (not required): Computer Vision: A Modern Approach by Forsyth & Ponce

Office hours: Thursday, 10am-12pm, Huang Basement

Office hours: Tuesday and Thursday, 12-1pm, Huang Basement

Office hours: Tuesday, 9:30-11:30am, Huang Basement

Office hours: Wednesday, 12:45-2:45PM, Huang Basement

For questions outside office hours, please use the class forum:

Lectures: Tuesdays and Thursdays 1:30pm to 2:50pm in 370-370

We may have a few sessions at irregular times see the Syllabus.

What do the following technologies have in common: robots that can navigate space and perform duties, search engines that can index billions of images and videos, algorithms that can diagnose medical images for diseases, or smart cars that can see and drive safely? Lying in the heart of these modern AI applications are computer vision technologies that can perceive, understand and reconstruct the complex visual world. Computer Vision is one of the fastest growing and most exciting AI disciplines in today’s academia and industry. This course is designed to open the doors for students who are interested in learning about the fundamental principles and important applications of computer vision. During the 10-week course, we will introduce a number of fundamental concepts in computer vision. We will expose students to a number of real-world applications that are important to our daily lives. More importantly, we will guide students through a series of well designed projects such that they will get to implement a few interesting and cutting-edge computer vision algorithms.

Homework: 80%

• HW0 (theoretical + programming): 8%

• HW1 (theoretical): 13%

• HW2 (programming and writeup): 13%

• HW3 (theoretical): 13%

• HW4 (programming and writeup): 13%

• HW5 (theoretical + programming): 20%

Extra credit: 2% for students who participate actively on piazza

We strongly recommend using LaTex, but also accept other typed or scanned assignment. However, students must be responsible for the legibility and we reserve the right to deduct points if the solution is not clear. Here is the template for Latex.

All assignments (with code attached) must be turned in to: GradeScope. Make an account and sign up for the class using the code: MBRJEM.

All code must also be submitted via email to [email protected] as a zip file "yourSUNetID_HW[0-5]_code.zip".

No paper submission is required for HWs.

Using Late Days:

• You have **5** free late days total.

• You can use up to **3** late days per assignment. (Homework will not be accepted more than 3 days late.)

• Please put number of late days used in the first page of your pdf.

• If you have used all of your late days, there is a 25% penalty for each day late.

• Explicitly mark the number of late days you use on an assignment if you are using late days. For example, if you turn it in by 5pm the next day, write "1 late day." If it's 5:01 pm the next day, write "2 late days." It is an honor code violation to write down the wrong time. (If you turn in late and don't write the number of days, we'll round up to 3.)

**We hope that you are familiar with:**

• College-level calculus (e.g. MATH 19 or 41) - You’ll need to be able to take a derivative, and maximize a function by finding where the derivative=0.

• Linear algebra (e.g. MATH 51) - We will use matrix transpose, inverse, and other operations to do algebra with matrix expressions. We’ll use transformation matrices to rotate/transform points, and we’ll use Singular Value Decomposition. (These topics are important for the homeworks, but if you are a quick learner you should be able to learn them during the class if you haven’t yet. We will have review sessions and provide review materials.)

• Basic probability and statistics (e.g. CS 109 or other stats course) - You should understand conditional probability, mean, and variance.

• We also require a decent amount of programming skills, such as entry-level Matlab, and the ability to work in the Linux environment. If you are unsure about your background, we encourage you to try out Problem Set 0, which is a “normalizing” problem set for the class. HW0 will help you gauge if CS131 is the right level for you.

## Instructor

Khatib's current research is in human-centered robotics, human-friendly robot design, dynamic simulations, and haptic interactions. His exploration in this research ranges from the autonomous ability of a robot to cooperate with a human to the haptic interaction of a user with an animated character or a surgical instrument. His research in human-centered robotics builds on a large body of studies he pursued over the past 25 years and published in over 200 contributions in the robotics field.

Prof. Khatib was the Program Chair of ICRA2000 (San Francisco) and Editor of ``The Robotics Review'' (MIT Press). He has served as the Director of the Stanford Computer Forum, an industry affiliate program. He is currently the President of the International Foundation of Robotics Research, IFRR, and Editor of STAR, Springer Tracts in Advanced Robotics. Prof. Khatib is IEEE fellow, Distinguished Lecturer of IEEE, and recipient of the JARA Award.