Math 462: Mathematical Foundations of Big Data

Spring 2018

Spring 2018

Instructor:
Todd Kuffner (kuffner who is @ wustl *dot* edu )

Lecture: 1:00 - 2:30, Tuesday/Thursday, Location: Cupples I, Room 215

Office Hours: Tuesday 11:00 - 12:00 and Thursday 10:00 - 11:00

Final Exam Date: May 8, 2018, 1:00 - 3:00 pm

Course Description: Mathematical foundations of data science. Core topics include: Probability in high dimensions; curses and blessings of dimensionality; concentration of measure; matrix concentration inequalities. Essentials of random matrix theory. Randomized numerical linear algebra. Data clustering. Linear dimension reduction. Other topics will be chosen by the instructor.

Prerequisite: Multivariable calculus (Math 233), linear or matrix algebra (Math 429 or 309), and multivariable-calculus-based probability and mathematical statistics (Math 493-494). Prior familiarity with analysis, topology, and geometry is strongly recommended. A willingness to learn new mathematics as needed is essential.

Textbook: There is no textbook for the course. The lectures are the primary reference for the course, but freely-available references for some topics may also be suggested.

Homework: There will be homework assignments which will consist of mathematical exercises and (mathematical) statistics exercises. You are strongly encouraged to write your solutions in LaTeX. If not, then handwritten submissions must be clear and organized.

Blackboard: During the semester, homework assignments, homework and midterm exam grades and any other course-related announcements will be posted to Blackboard or sent by email using Blackboard.

Attendance: Attendance is required for all lectures. The student who misses a lecture is responsible for any assignments and/or announcements made.

Grades: The grade for the course will be based on Homework (20%), Exam I (20%), Exam 2 (20%) and the Final Exam (40%).

Final Course Grade: The letter grades for the course will be determined according to the following numerical grades on a 0-100 scale.

Other Course Policies: Students are encouraged to look at the Faculty of Arts & Sciences policies.

Lecture: 1:00 - 2:30, Tuesday/Thursday, Location: Cupples I, Room 215

Office Hours: Tuesday 11:00 - 12:00 and Thursday 10:00 - 11:00

Final Exam Date: May 8, 2018, 1:00 - 3:00 pm

Course Description: Mathematical foundations of data science. Core topics include: Probability in high dimensions; curses and blessings of dimensionality; concentration of measure; matrix concentration inequalities. Essentials of random matrix theory. Randomized numerical linear algebra. Data clustering. Linear dimension reduction. Other topics will be chosen by the instructor.

Prerequisite: Multivariable calculus (Math 233), linear or matrix algebra (Math 429 or 309), and multivariable-calculus-based probability and mathematical statistics (Math 493-494). Prior familiarity with analysis, topology, and geometry is strongly recommended. A willingness to learn new mathematics as needed is essential.

Textbook: There is no textbook for the course. The lectures are the primary reference for the course, but freely-available references for some topics may also be suggested.

Homework: There will be homework assignments which will consist of mathematical exercises and (mathematical) statistics exercises. You are strongly encouraged to write your solutions in LaTeX. If not, then handwritten submissions must be clear and organized.

Blackboard: During the semester, homework assignments, homework and midterm exam grades and any other course-related announcements will be posted to Blackboard or sent by email using Blackboard.

Attendance: Attendance is required for all lectures. The student who misses a lecture is responsible for any assignments and/or announcements made.

Grades: The grade for the course will be based on Homework (20%), Exam I (20%), Exam 2 (20%) and the Final Exam (40%).

Final Course Grade: The letter grades for the course will be determined according to the following numerical grades on a 0-100 scale.

A+ |
impress me |
B+ |
[87, 90) |
C+ |
[77, 80) |
D+ |
[67, 70) |
F |
[0,60) |

A |
93+ |
B |
[83, 87) |
C |
[73, 77) |
D |
[63, 67) |
||

A- |
[90, 93) |
B- |
[80, 83) |
C- |
[70, 73) |
D- |
[60, 63) |

Other Course Policies: Students are encouraged to look at the Faculty of Arts & Sciences policies.

- Academic integrity: Students are expected to adhere to the University's policy on academic integrity.
- Auditing: There is an
option to audit, but this
still involves enrolling in the course. See the Faculty of Arts &
Sciences policy
on auditing.
Auditing students will still be expected to attend all
lectures and compete all required coursework and exams. A course grade
of 75 is required for a successful audit.

- Collaboration: Students are encouraged to discuss homework with one another, but each student must submit separate solutions, and these must be the original work of the student.
- Exam conflicts: Read the
University policy.
The exam dates for this course are posted before the semester begins,
and thus you are expected to be present at all exams.

- Late homework: Only by
prior arrangement. If a valid reason for an exception is not presented
at least 36
hours before a homework due date, then it will not be accepted late (a
zero will be given for that assignment).

- Missed exams: There are no make-up exams. For valid excused absences with midterm exams - such as medical, family, transportation and weather-related emergencies - the contribution of that midterm to the final course grade will be redistributed equally to the other midterm exam and final exam. Students missing both midterm exams and/or the final exam cannot earn a passing grade for the course.