MAE 289B. Mathematical Analysis with Applications

Announcements

In this website you will find some preliminary information about this course. All the class material will be shared via canvas. Access to the canvas section here.

Contact Information

Instructor	Office	Phone	Email
Prof. Sonia Martínez	FAH 3302	858-822-4243	soniamd at ucsd dot edu

Office Hours

Instructor	Day	Time	Location
Sonia Martinez	Tues	3:15pm - 4:15pm	TBA

Schedule of Classes

Lecture	Day	Time	Location
Regular lecture	Tues/Thurs	9:30 - 11:00am

Course description

This course is the second one of a series of three, covering miscellaneous topics of mathematical reasoning, mathematical analysis for real/vector-valued functions of one and/or several variables. Currently, the level of mathematics necessary for a successful path through much of the MAE PhD graduate curriculum is above that with which students typically arrive. The goal of this sequence is to bring you to the point where you can more easily handle the material in more advanced courses of the program. While doing so, we will aim to present applications of the theory to dynamics systems, optimization, and control. A special emphasis will be placed on proof techniques. The course is math intensive does not cover linear algebra in detail, this is done through courses such as 280a and 280b. Finally, note that if you are enrolled in the new MS program, you may not need to take this course. (Of course, you still may take it if you like.) The topics to be covered in this particular class refer to measure, integration with main applications to probability.

Prerequisites

Real and complex number systems, basic topology (open, closed, neighborhood, compact, metric spaces, connected sets) and continuity will be assumed.

Syllabus

The course syllabus can be found here

Assignments and Grades

A homework assignment per week. The homework will carry 100 percent of the grade.

Collaboration Policy

You are encouraged to work with other students on your assignments, and to help other students complete their assignments, provided that you comply with the following conditions:

• Honest representation: The material you turn in for course credit must be a fair representation of your work. You are responsible for understanding and being able to explain and duplicate the work you submit. Group submissions are not allowed in this course, and each student should submit their own individual assignment, written in their own words. The same happens with programming exercises: please do not submit exact copies of programming solutions, the autocorrection tool in Gradescope checks for plagiarism.
• Active involvement: You must ensure that you are an active participant in all collaborations, and are not merely dividing up the work or following along while another student does the work. For example, copying another student's work without actively being involved in deriving the solution is strictly prohibited. To avoid misunderstandings, please turn in solutions written in your own words, not an exact copy of what someone else submits.
• Give help appropriately: When helping someone, it is important not to simply give them a solution, because then they may not understand it fully and will not be able to solve a similar problem next time. It's always important to take the time to help someone think through the problem and develop the solution. Often, this can be accomplished by asking them a series of leading questions.
• If in doubt, ask your instructor: Be sure to ask in advance if you have any doubts about whether a certain type of collaboration is acceptable.

Note on Academic Dishonesty

No form of academic dishonesty will be tolerated, this specially refers to homework and plariagism.
In this course, the use of ChaptGPT or other GenAI tools to solve homework problems is not allowed and constitutes cheating. To avoid problems, please make sure you report who you work with when doing the homework, and do not turn in exact homework copies. Copying from previous homework solutions is also considered cheating. For the definition of academic dishonesty and its consequences refer to the Student Conduct Code available at the website https://academicintegrity.ucsd.edu