Click here to apply to PI4 for Summer 2020.

The program has three components this summer: Computational Bootcamp, Professional Development Sessions, and Internships.

1. Computational Mathematics Bootcamp

June 1-12 (online), focusing on Data Science with R and Python. Instructor: Uma Ravat.

2. Professional Development Sessions. Three or four professional development sessions, at times to be determined during June and July. Participation is expected of all students receiving Internship funding. [Professional development events canceled in view of COVID-19 disruptions.]

3. Internships.Various dates. Hosts to be arranged.

Computational Bootcamp 2019 (9 days on Python, R and data science)

Courses from previous years – 2018, 2017, 2016, 2015, 2014

Click here to apply to PI4 for Summer 2019.

The program has four components. Students early in the graduate program usually do the Linear Algebra Working Group, Computational Bootcamp, and Prepare/Train Group. Students later in the graduate program usually do the Computational Bootcamp and an Internship.

1. Linear Algebra Working Group

May 15-17 (239 Altgeld Hall), led by Elliot Kaplan.

2. Computational Mathematics Bootcamp

Part I: May 20-31 (239 Altgeld Hall), led by Uma Ravat focusing on Data Science with R and Python.

3. Prepare and Train Group – Sociophysics: Bias and homophily in professional hierarchies, and Models of social group competition
Dates: June 3-July 15 (with holiday on July 4)
Location: 159 Altgeld Hall has been booked 9am-1pm each day
Instructor: Prof. Sara Clifton

The program is a “Research Experience for Graduate Students” style endeavor: after a series of introductory lectures, the students form small groups (2-5 people) to work on open-ended, interconnected problems. Students will work during the first three weeks on models for “Bias and homophily in professional hierarchies” (building on this paper). Then the groups will change around for the second three weeks, tackling problems on “Models of social group competition” (where references include this and this).

Overview. The goal is to guide students through the transition from working on “canned” problems to tackling open-ended problems and formulating the problems themselves. We expect the group work to involve a mixture of computational experiments (to generate conjectures) and theory (to prove them).

Professional Development Sessions. New to the program this year are four professional development sessions, on Wednesday afternoons during June. Participation is expected of all students in the Prepare/Train program.

• •Exploring Broad Careers in Mathematics (Derek Attig, Director of Career Development, Graduate College), Wednesday June 5, 3:30-5:00pm in 308 Coble Hall
• •Managing Large and Complex Projects (Mike Firmand, Assistant Director for Employer Outreach, Graduate College), Wednesday June 12, 3:30-5:00pm in 308 Coble Hall
• •Data presentation/visualization (Megan Ozeran, Data Analytics & Visualization Librarian, University Library), Wednesday June 19, 3:30-5:00pm in 308 Coble Hall
• •Talking about Your Research (Emily Wuchner, Thesis Coordinator, Graduate College), Wednesday June 26, 3:30-5:00pm in 308 Coble Hall

Refreshments provided.

4. Internships

Various dates. Hosts to be arranged. Interns funded through PI4 are strongly encouraged to participate in the professional development events listed above, provided their employer grants permission to make up the hours at another time during the week.

The 2019 Linear Algebra Workshop was offered as part of the PI4 program, and was be led by Elliot Kaplan, building on materials developed in previous years by Stef Klajbor Goderich. The goal of the workshop is to review and learn some advanced linear algebra with an eye towards applications and the Computational Bootcamp, which runs immediately after this workshop.

What is the format of the workshop?
Students work in groups through the worksheets (see files below). Informal presentations and discussions on the most important problems occur throughout the day. The style is informal, with students working in a collaborative environment.

How are the worksheets structured?
Each day’s worksheet contains a list of definitions, theorems, and exercises (about 40 each day). Some of the problems were modified from those in the references, while others are problems written for this working group.

• Day 1 Worksheet    (Day1_Sheet)
  Projections and the Gram-Schmidt Process
  QR Factorization
  Least-squares
  Linear Models: Regression
• Day 2 Worksheet    (Day2_Sheet)
  Diagonalization
  Symmetric matrices
  Spectral Theorem
  Quadratic Forms
  Singular Value Decomposition
• Day 3 Worksheet    (Day3_Sheet)
  Principal Component Analysis and Dimensional Reduction
  Brief look at Markov Chains
  LU Factorizations
  Duals and annihilators
  Some multilinear algebra

Acknowledgment
These Linear Algebra Workshop materials may be freely used by others. We ask that when materials are re-used, the following statement be included:

These materials were created by Stefan Klajbor Goderich at the University of Illinois and edited by Elliot Kaplan, with support from National Science Foundation grant DMS 1345032 “MCTP: PI4: Program for Interdisciplinary and Industrial Internships at Illinois.”

Computational Bootcamp 2018 – Part 1 (6 days on data science)
Computational Bootcamp 2018 – Part 2 (3 days on Mathematica fundamentals)

Courses from previous years – 2017, 2016, 2015, 2014

The program has four components. Students early in the graduate program usually do the Linear Algebra Working Group, Computational Bootcamp, and Prepare/Train Group. Students later in the graduate program usually do the Computational Bootcamp and an Internship.

1. Linear Algebra Working Group

May 16-18 (239 Altgeld Hall), led by Stefan Klajbor Goderich

2. Computational Mathematics Bootcamp

Part I: May 21-26 (239 Altgeld Hall) with focus on Data Science, led by David LeBauer.

Part II: May 30-June 1 (239 Altgeld Hall) with focus on Mathematica Fundamentals, led by A. J. Hildebrand

3. Prepare and Train Group – Algorithms for Analytic Combinatorics
Dates: June 4-July 13 (with holiday on July 4)
Location: 159 Altgeld Hall (room booked in mornings)
Instructor: Stephen Melczer (U. of Pennsylvania)

The program is a “Research Experience for Graduate Students” style endeavor: after a series of introductory lectures, the students form small groups (2-5 people) to work on open-ended interconnected problems.

Overview. The goal is to guide students through the transition from working on “canned” problems to tackling open-ended problems and formulating the problems themselves. We expect the group work to involve a mixture of computational experiments (to generate conjectures) and theory (to prove them).

One of the draws of combinatorics is its ability to draw on, motivate, and even push forward diverse areas of mathematics and computer science. The focus of this program will be to study the methods of analytic combinatorics – a field drawing inspiration from complex analysis, differential geometry, and algebraic geometry – from the perspective of computer algebra.

Students will begin by learning the underlying theory and implementing algorithms which have been previously described at a theoretical level. Later, students will engage with open problems of both a theoretical and computational nature, and examine new applications of this fast-growing theory. A wide range of problems of varying difficulty will be available for students with different backgrounds.

Topics include the new theory of analytic combinatorics in several variables, effective enumeration results for power series coefficients of algebraic functions, and decompositions of multivariate rational functions. Potential applications touch on areas of queuing theory, representation theory, theoretical computer science, transcendence theory, probability theory, and (of course) combinatorics.

A more detailed statement of problems can be downloaded here.

4. Internships

Various dates. Hosts to be arranged.

The 2017 Linear Algebra Workshop was offered as part of the PI4 program. The goal of the workshop was to review and learn some advanced linear algebra with an eye towards applications and the Computational Bootcamp, which ran immediately after this workshop.

What is the format of the workshop?
Students work in groups through the worksheets (see files below). Informal presentations and discussions on the most important problems occur throughout the day. The style is informal, with students working in a collaborative environment.

How are the worksheets structured?
Each day’s worksheet contains a list of definitions, theorems, and exercises (about 40 each day). Some of the problems were modified from those in the references, while others are problems written for this working group.

• Day 1 Worksheet    (tex file, tex label index, pdf file)
  Projections and the Gram-Schmidt Process
  QR Factorization
  Least-squares
  Linear Models: Regression
• Day 2 Worksheet    (tex file, tex label index, pdf file)
  Diagonalization
  Symmetric matrices
  Spectral Theorem
  Quadratic Forms
  Singular Value Decomposition
• Day 3 Worksheet    (tex file, tex label index, pdf file)
  Principal Component Analysis and Dimensional Reduction
  Brief look at Markov Chains
  LU Factorizations
  Duals and annihilators
  Some multilinear algebra

The “tex label index” files are useful when editing the tex files, as they list the labels used in the tex code.

Acknowledgment
These Linear Algebra Workshop materials may be freely used by others. We ask that when materials are re-used, the following statement be included:

These materials were created by Stefan Klajbor Goderich at the University of Illinois, with support from National Science Foundation grant DMS 1345032 “MCTP: PI4: Program for Interdisciplinary and Industrial Internships at Illinois.”

Click here to apply to PI4 for Summer 2017.

Linear Algebra Working Group

May 22-24, in 239 Altgeld Hall

Computational Mathematics Bootcamp:

May 26-June 9, in 239 Altgeld Hall; note Memorial Day holiday on Monday May 29

Prepare and Train Group – Machine Learning: Algorithms and Representations
Dates: Monday June 12 through Friday July 21; note Independence Day holiday on Tuesday July 4
Location: TBD
Instructors: Maxim Raginsky (Department of Electrical and Computer Engineering) and Matus Jan Telgarsky (Department of Computer Science)

The program is a “Research Experience for Graduate Students” style endeavor: after a series of introductory lectures, the students form small groups (2-5 people) to work on open-ended interconnected problems.

The goal is to guide students through the transition from working on “canned” problems to tackling open-ended problems and formulating the problems themselves. We expect the group work to involve a mixture of computational experiments (to generate conjectures) and theory (to prove them).

The topics will focus on probabilistic and approximation-theoretic aspects of machine learning, with emphasis on neural networks. We will introduce the probabilistic formulation of machine learning and relate the performance of commonly used learning algorithms (such as stochastic gradient descent) to the concentration of measure phenomenon. Problems of varying levels of difficulty will revolve around several open questions pertaining to stability and convergence of stochastic gradient descent. We will also cover several results characterizing neural network function classes, for instance results saying that neural networks can fit continuous functions, that neural networks gain in power with extra
layers, and that neural networks can model polynomials. Open questions will cover more nuanced aspects of adding layers, as well as other neural net architectures, for instance convolutional and recurrent neural networks.

Internships

Various dates. Hosts to be arranged.