# Teaching

## Fall 2024 courses - quick facts

Math 431 Computational Algebraic Geometry &

Math 530 Applied Computational Algebra

Mondays & Wednesdays 10:00am - 11:15pm

At a glance:

Input:

openness to new ideas in mathematics,

critical thinking & skepticism,

enthusiasm for learning new concepts.

Output:

general understanding of nonlinear algebra,

experience in solving systems of polynomial equations,

an understanding of the state of the art in symbolic computation.

Interactive, with participation being a grade component:

AhaSlides! (or similar) interactive quizzes for working through examples in the lectures;

Slack as the main communication platform (wiki-style, social style, quick, easy to use).

Respectful of many facets of humankind (share your culture! share your experience! you are valued!) and inclusive (choose your method of participation: anonymous (yes, it counts for credit), vocal, written, share your identity, ... This is your class. Make it work for you.

### What is this course about?

Be singular*! Learn about solving polynomial systems in math 431/530

This is a cross-listed course in non-linear algebra. It covers the basics of how to solve systems of polynomial equations, a task you'd think everyone knows how to do... but since this is about nonlinear systems, it is a surprisingly difficult problem with a rich geometric backbone and open problems in algorithm design. The course will offer you a chance to learn the theory -- from first principles -- of non-linear algebra, which is increasingly important in applications from statistics to engineering and geometric modeling. We will focus on the theory to enable you to study an applied problem of your choice through a group course project.

*What is a singular point?

On a mathematical surface, it is a point that stands out; making life difficult, and the math more interesting. The opposite of a smooth, regular point, on which algorithms converge fast, where statistical modeling questions have straightforward answers, where there are no `wrinkles'.

By taking Math 431/530 elective, you become a singular point in the student body.

Be different.

Join me on this journey to learn more in Fall 2024.

## Spring 2024 COURSES - QUICK FACTS

Math 474 - Probability and Statistics [LINK to course homepage]

Mondays & Wednesdays 10:00am - 11:15am

At a glance:

Input:

interest in reasoning with data and making inference under uncertainty,

critical thinking & skepticism & an open mind,

enthusiasm for learning new concepts.

Output:

an understanding of basic notions in probability and statistics,

recognition of where random variables and uncertainty surround us in daily life,

basic proficiency in open-source software for data analysis.

Textbook: Walpole, Meyers, Meyers, Ye, Probability and Statistics for Engineers and Scientists, 9th ed., Prentice Hall

Topics: Here is a link to the department syllabus.

As I say on day 1 of each semester:

This can be your class. Make it work for you.

Note: I am not teaching in Fall 2023 due to DOE grant research activity.

In addition, I will be visiting the IMSI long program on Algebraic Statistics as a lead organizer.

## Spring 2023 courses - quick facts

Math 561 Algebraic and Geometric Methods in Statistics

Mondays & Wednesdays 11:25am - 12:40pm

At a glance:

Input:

interest in applied data analysis and new techniques for developing statistical models,

critical thinking & skepticism,

enthusiasm for learning new concepts.

Output:

an understanding of nonlinear algebra and its impact in statistics,

deep knowledge of exponential families and what role model structure plays in applied data analysis,

experience in working with non-traditional data such as sparse networks in an applied field,

an understanding of the state of the art in testing model/data fit.

Interactive and not a traditional exam-based course:

Homework;

Group projects;

Communication and presentation an essential element for PhD students.

As I say on day 1 of each semester:

This can be your class. Make it work for you.

### What is this course about?

Algebraic statistics as a field started in the 1990s at a convergence point between computational algebra and mathematical statistics. The motivation for this set of blended tools was applied analysis of categorical data and design of experiments. The early days saw a flourish of theoretical research about algebraic, geometric, and combinatorial methods that can be useful in statistics. In the recent decade, there has been a strong push for applications, as detailed for example in this overview paper.

The course syllabus can be found here.

No exams are planned for this graduate elective course.

## Fall 2022 courses - quick facts

Math 431 Computational Algebraic Geometry &

Math 530 Applied Computational Algebra

Tuesdays & Thursdays 11:25am - 12:40pm

At a glance:

Input:

openness to new ideas in mathematics,

critical thinking & skepticism,

enthusiasm for learning new concepts.

Output:

general understanding of nonlinear algebra,

experience in solving systems of polynomial equations,

an understanding of the state of the art in symbolic computation.

Interactive, with participation being a grade component:

AhaSlides! (or similar) interactive quizzes for working through examples in the lectures;

Campuswire as the main communication platform (wiki-style, social style, quick, easy to use).

Respectful of many facets of humankind (share your culture! share your experience! you are valued!) and inclusive (choose your method of participation: anonymous (yes, it counts for credit), vocal, written, share your identity, ... This is your class. Make it work for you.

### What is this course about?

Be singular*! Learn about solving polynomial systems in math 431/530

This is a cross-listed course in non-linear algebra. It covers the basics of how to solve systems of polynomial equations, a task you'd think everyone knows how to do... but since this is about nonlinear systems, it is a surprisingly difficult problem with a rich geometric backbone and open problems in algorithm design. The course will offer you a chance to learn the theory -- from first principles -- of non-linear algebra, which is increasingly important in applications from statistics to engineering and geometric modeling. We will focus on the theory to enable you to study an applied problem of your choice through a group course project.

*What is a singular point?

On a mathematical surface, it is a point that stands out; making life difficult, and the math more interesting. The opposite of a smooth, regular point, on which algorithms converge fast, where statistical modeling questions have straightforward answers, where there are no `wrinkles'.

By taking Math 431/530 elective, you become a singular point in the student body.

Be different.

Join me on this journey to learn more in Fall 2022.

### Let's have a conversation!

My teaching goal is to re-frame all of our learning as a conversation. I've learned from toddlers recently: nobody should think of themselves an expert vs. novice; we are all discovering together, exchanging ideas, and building upon them.

While it is extremely difficult to reframe entire semester-long courses from this point of view in the present educational system, I promise to - at least - keep lectures interactive during the semester. One example of what this means is the use of interactive quiz slides throughout the lecture, such as these slides - they are not presented all at once, but dispersed around the lecture.

### Advice for graduate students

### Fall 2022

Math 431/530 Nonlinear algebra (computational algebraic geometry)

### AY 21/22

Sabbatical research year.

### Spring 2021

Stat 514 / ITMD/ITMS 514 Applied computational statistics for analytics

Math 563 Mathematical statistics

### Fall 2020

Stat 514 / ITMD/ITMS 514 Applied computational statistics for analytics

Math 431/530 Nonlinear algebra (computational algebraic geometry)

### Older

For a full list of courses I've taught, go here: courses taught at IIT, at Penn State, at UIC, at UK.