Syllabus Stat 243Aut2018 PDF

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STAT 24300 - 30750

NUMERICAL LINEAR ALGEBRA

Autum Autumn n 2018

T-Th 2:00 – 3:20 pm in MS 112

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INSTR INSTRUCTOR: UCTOR: Fatma Terzioglu EE-MAIL: MAIL: [email protected] WEBPAGE WEBPAGE:: http://www.stat.uchicago.edu/~fterzioglu/

OFFICE OFFICE:: Jones 316 OFF OFFICE ICE HOU HOURS RS RS:: T 3:20-4:00 pm in MS112 Th 1:00-2:00 pm in MS122

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TEACHING ASS ASSISTANTS: ISTANTS: EE-MAIL: MAIL: OFFICE: OFFICE H HOURS OURS OURS:: PROB PROBLEM LEM SE SESSION SSION SSIONS S:

Rebecca Kotsonis Zhipeng Lou [email protected] [email protected] Jones 203/204 Jones 203/204 M 3:30-5:30 pm in Jones 304 F 9:00 – 11:00 am in Jones 226 W 3:30-5:00 pm in Eckhart 133 (Starting Oct. 10)

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CATALOG DES DESCRIP CRIP CRIPTIO TIO TION: N: This course is devoted to the basic theory of linear algebra and its significant applications in scientific computing. The objective is to provide a working knowledge and hands-on experience of the subject suitable for graduate level work in statistics, econometrics, quantum mechanics, and numerical methods in scientific computing. Topics include Gaussian elimination, vector spaces, linear transformations and associated fundamental subspaces, orthogonality and projections, eigenvectors and eigenvalues, diagonalization of real symmetric and complex Hermitian matrices, the spectral theorem, and matrix decompositions (QR, Cholesky and Singular Value Decompositions). Systematic methods applicable in high dimensions and techniques commonly used in scientific computing are emphasized. Students enrolled in the graduate level STAT 30750 will have additional work in assignments, exams, and projects including applications of matrix algebra in statistics and numerical computations implemented in MATLAB or R. Some programming exercises will appear as optional work for students enrolled in the undergraduate level STAT 24300. PREREQ PREREQUI UI UISIT SIT SITES: ES: MATH 16300 or 19520 or 20000 or 20500 or 20900. Or graduate student in Statistics or Financial Mathematics. COURS COURSE E WEBPAGE WEBPAGE:: The course webpage is on Canvas. TEXTBOOK: Recommended textbook: Linear Algebra and Its Applications by G. Strang (2006, 4th ed.) Additional reference for S30750: Fundamentals of Matrix Computation by D. Watkins (2010, 3rd ed. or 2002 2nd ed.) COURS COURSE E GOALS GOALS:: After successfully completing the course, you will have a good understanding of the following topics and their applications: • Systems of linear equations • Determinants and their properties • Row reduction and echelon forms • Eigenvalues and eigenvectors • Matrix operations, including inverses • Diagonalization of a matrix • Linear dependence and independence • Symmetric matrices • Subspaces and bases and dimensions • Positive definite matrices

• • •

Orthogonal bases and orthogonal projections Gram-Schmidt process Linear models and least-squares problems

• • •

Similar matrices Linear transformations Singular Value Decomposition

IMPORTANT DATES DATES:: October ber 1 (Monday) First day of Classes: Octo Midterm Ex am: No Novve mb mber er 1 (Thursday during class)

Final Exam: December 13 (Thursday) EXAMINA EXAMINATION TION TIONS: S: Only univers ity excused absences will be accepted for makeup exams. The final exam is cumulative, and will be held on December 13 from 1:30 - 3:30 pm in MS 112. Students are required to bring their University of Chicago Student ID to all exams. If there are any questi ons regarding grading of exams they should be asked of the instructor directly within two class days of receiving the graded paper. QUIZZ QUIZZE E S: There will be some in-class and some take-home quizzes along the way. In-class quizzes will be given during the last ten minutes of the class. The instructor will announce at the beginning of the class if there will be a quiz that day. HOM HOMEWOR EWOR EWORK: K: Homework assignments will be posted on the course webpage in Canvas, and will be due in class in a week. Only paper submissions will be accepted. The code file of 30750 should be submitted with the name YourlastnameFirstnameHw#.m (or .r) to Canvas, under “30750 Assignment # code submission”. If you are unable to attend the class to submit your homework, you can leave it to the course mailbox in Jones 222 during regular hours any daybefore the due date. Online submission is allowed only in the case of a health Latee probl roblem em set setss will not be ac accep cep cepted tedexcept health emergencies. Completed assignments should emergency. Lat be clearly written or typed instan standar dar dard d letter siz sized ed paper, staple stapled, d, and with a cov cover er page iinc nc ncludi ludi luding ng you yourr na name me your ur assig assignm nm nments ents and STAT2 STAT24300 4300 or STAT3 STAT307 07 0750 50 clear clearly ly marke marked. d. You are required to write up yo independently. The final project for STAT30750 needs to be typed. Our teaching assistants will be available during office hours to discuss questions you may have about the problem set.You are enco encou u rag raged ed to discuss the h homew omew omework ork pr prob ob oble le lems ms iin n Piaz Piazzz a wi with th thout out sh shar ar arin in ingg th thee so soluti luti lution on ons. s. GRADI GRADING NG POL POLIC IC ICY Y: Students are expected to attend classes, participate in discussions and quiz questions, complete assignments and take exams. Your final grade in this course will consist of a midterm exam, one cumulative final, homewor k, and quizzes. The breakdown of pointswill be as follows:

HW + Quiz

30%

Midterm

30%

Final Exam

40%

COURS COURSE E POLICIES POLICIES:: A ttendance is strongly encouraged. To make up a quiz or exam, you must have proof of a university excused absence. If you know you will be absent ahead of time, you need to email the instructor

before the day youwill be ab sent telling her your reason. In the case of an unexpected but excused absence (such as an accident or emergency), please email the instructor within two days letting her know the reason

for your absence. GETTI GETTING NG HEL HELP P OUT OUTSIDE SIDE OF CL CLASS ASS ASS:: There will be weekly prob problems lems s essi essions ons run by the TA’s on Wednesda Wednesdays ys fr from om 3: 3:30 30 30-5: -5: -5:0 0 0 pm i n E ck ckh har artt 1 33. Also, feel free to attend the instructor’s or the TAs’ office hours to get help on homework, or to clarify something that you don't understand. We'll also usePiazza for questions and discussion. Our class page is https://piazza.com/class/jn155i4mapk2cs, or use the Piazza tab from the navigation menu in Canvas.

AMERICANS WITH DISABILITI DISABILITIES ES ACT: The Ameri cans with Disabilities Act (ADA) is a federal antidiscrimination statute that p rovides comprehensive civil rights prot ection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Student Disability Services (https://disabilities.uchicago.edu/). ACADEMI ACADEMIC C INT INTEGRITY EGRITY EGRITY:: Students are strongly encouraged to work together on homework assignments, but each student must submit his or her own writeup. Plagiarism of material written by classmates, book or article authors, or web posters is prohibited. Students must work independently on exams. Academic integrity will be strictly enforced. For additional information please visit: https://college.uchicago.edu/advising/academic-integritystudent-conduct COPYRIG COPYRIGHT HT POLICY POLICY:: Any material the instructor produce throughout the cour se is copyrighted, including

(but not limited to) syllabi, quizzes, worksheets, exams, reviews, or any in-classma terial. TENTATIVE COURSE SCHEDU SCHEDULE LE LE:: Week 1

Date Oct. 2, 4

Topics Introduction. Linear equations and geometry in the space Rn. Gaussian elimination and basic matrix algebra. Vector spaces.

Textbook 1.1-1.4, 2.1

2

Oct. 9, 11

Introduction. Matrix operation and invertible matrices. Vector spaces and subspaces.

1.5, 1.6, 2.1, 2.2

3

Oct. 16, 18

Linear independence basis and dimension. Null space, column space, kernel and image

2.3, 2.4

4

Oct. 23, 25

Linear transformations. Change of basis. Orthogonality. Projection.

2.6, 3.1-3.3

5

Oct. 30,

3.3, 3.4, 4.1, 4.2

Nov. 1

Projections and least squares, Gram-Schmidt and QR decomposition. Introduction to the determinant Midterm Exam

Nov. 6, 8

Formulas, computation and significance of the determinant.

4.3, 4.4

6

Eigenvalues and eigenvectors. 7

Nov. 13, 15

Diagonalizable matrices. Difference equations, powers and exponentials of matrices.

5.1-5.4

8

Nov. 20, 22

Complex matrices and the Spectral theorem. Similarity transformations.

5.5, 5.6

9

Nov. 27, 29

Positive definite matrices and tests, Cholesky decomposition. Singular Value Decomposition (SVD).

6.1-6.3

10

Dec. 4

SVD and its applications

6.3

11

Dec. 14

Final exam 1:30 - 3:30 pm, MS 112...