# Teaching

## Fall 2024 courses - quick facts

Math 431 Computational Algebraic Geometry &
Math 530 Applied Computational Algebra

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.

### 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.

## Spring 2024 COURSES - QUICK FACTS

Math 474 - Probability and Statistics [LINK to course homepage

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.

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

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.

### 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

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.

### 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.

### 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.

Studying tips: