# IAP 2023 Classes

## For-credit subjects:

Check out the course catalog at http://student.mit.edu/catalog/m18a.html. You can use the Subject Search functionality to limit the search to IAP listings or find Math's IAP offerings here: http://student.mit.edu/catalog/search.cgi?search=18&when=J. Our main offerings in Mathematics are:

### 18.02A Calculus

- Prof Bill Minicozzi and staff
- Jan. 9 - Feb. 3
- MTWRF1
- TR10-11.30 or TR2-3.30 +final

*This class will meet in person on campus. Lectures will be held in E25-111.*

12 units (only 6 will count toward IAP credit limit)

This is the second half of 18.02A and can be taken only by students who took the first half in the fall term; it covers the remaining material in 18.02.

### 18.031 System Functions and the Laplace Transform

- Dr Keaton Burns
- Jan. 9-27
- MWF 10-12
- This class will be conducted in hybrid mode, with students encouraged to attend in person in room 2-142, but a zoom option will be made available.

3 units (P/D/F graded)

Studies basic continuous control theory as well as representation of functions in the complex frequency domain. Covers generalized functions, unit impulse response, and convolution; and Laplace transform, system (or transfer) function, and the pole diagram. Includes examples from mechanical and electrical engineering.

### 18.095 Mathematics Lecture Series

- MWF1-2.30
- R10.30-12 or R1-2.30
- This class will meet in person on campus. Lectures will be held in 2-190, and many should also be recorded. Recitations will meet in 2-131.

6 units (P/D/F graded)

Ten lectures by mathematics faculty members on interesting topics from both classical and modern mathematics. All lectures accessible to students with calculus background and an interest in mathematics. At each lecture, reading and exercises are assigned. Students prepare these for discussion in a weekly problem session.

#### Lecture Schedule

Monday, January 9 | G. Staffilani | A small window on wave turbulence theory |

Wednesday, January 11 | J. Kepner & H. Jananathan | Mathematics of Big Data and Machine Learning |

Friday, January 13 | E. Mossel | Mafia, War and Random Walks |

Wednesday, January 18 | D. Alvarez-Gavela | Wavefronts and their caustics |

Friday, January 20 | J. Bush | Surface tension |

Monday, January 23 | K. Burns | Numerical simulations with exponential accuracy |

Wednesday, January 25 | P. Rigollet | Win the presidential election with game theory and couplings |

Friday, January 27 | A. Sutherland | Elliptic curve cryptography |

Monday, January 30 | P. Seidel | The sounds of shapes |

Wednesday, February 1 | L. Demanet | The "forgotten" 18.03 topic: Prony’s method |

### 18.S096 Special Subject in Mathematics: Matrix Calculus for Machine Learning and Beyond

**Website:**https://github.com/mitmath/matrixcalc/blob/main/README.md- Profs Alan Edelman and Steven Johnson
- Jan 17 - Feb 3
- MWF 11am-1pm
- This class will meet in 2-190.

3 units

We all know that calculus courses such as 18.01 and 18.02 are univariate and vector calculus, respectively. Modern applications such as machine learning require the next big step, matrix calculus.

This class covers a coherent approach to matrix calculus showing techniques that allow you to think of a matrix holistically (not just as an array of scalars), compute derivatives of important matrix factorizations, and really understand forward and reverse modes of differentiation. We will discuss adjoint methods, custom Jacobian matrix vector products, and how modern automatic differentiation is more computer science than mathematics in that it is neither symbolic nor finite differences.

Prereq: Linear Algebra such as 18.06 and multivariate calculus such as 18.02

### 18.S097 Special Subject in Mathematics: Introduction to Julia for Data Science

- Profs Alan Edelman, Bogumił Kamiński, and Przemysław Szufel
- Jan 17 - 20
- TWRF 11am-12:30; 1pm-3pm
- This class will meet in 2-131.

3 units

Data analysis has become one of the core processes in virtually any professional activity. The collection of data becomes easier and less expensive, so we have ample access to it.

The Julia language which was designed to address the typical challenges that data scientists face when using other tools. Julia, like Python, supports an efficient and convenient development process. At the same time, programs developed in Julia have performance comparable to C.

During this short course you will learn how to build data science models using Julia. Moreover, we will teach you how to deploy such model in production environments and scale the computations beyond a single computer.

This course does not require from the participants prior detailed knowledge of advanced machine learning algorithms not the Julia programming language. What we assume is basic knowledge data science tools (like Python or R) and techniques (like linear regression, basic statistics, plotting).

All course materials are available on a dedicated GitHub repository https://github.com/pszufe/MIT_18.S097_Introduction-to-Julia-for-Data-Science.

Schedule

- Day 1 (Tuesday, Jan 17, 2023)
- 11:00-12:30 Your first steps with Julia
- 13:00-15:00 Working with tabular data

- Day 2 (Wednesday, Jan 18, 2023)
- 11:00-12:30 Classical predictive models
- 13:00-15:00 Advanced predictive models using machine learning

- Day 3 (Thursday, Jan 19, 2023)
- 11:00-12:30 Solving optimization problems
- 13:00-15:00 Mining complex networks

- Day 4 (Friday, Jan 20, 2023)
- 11:00-12:30 Deployment in production environments
- 13:00-15:00 Scaling computations using parallel computing

Location: Room 2-131 on MIT Campus. See http://whereis.mit.edu/?mapterms=2-131 for location.

Instructors: Bogumił Kamiński, Łukasz Kraiński, Przemysław Szufel, Bartosz Witkowski, Sebastian Zając, Mateusz Zawisza

**Grading**

You can register for this course for credit. The contact point regarding the registration process is Professor Alan Edelman, Julia Lab Research Group Leader.

The evaluation of the course will be based on assessment of a homework that will be distributed during the last day of the course and should be sent back to Przemysław Szufel () no later than after one week.

### 18.S190 Special Subject in Mathematics: Introduction to Metric Spaces

- Paige Dote, , Faculty Advisor: Prof Larry Guth
- Jan 9-26
- TR 9:00-10:30
- This class will meet in person on campus in room 2-131. We hope to record most meetings for those who must occasionally miss a class.

3 units (P/D/F-graded)

Covers metrics, open and closed sets, functional spaces, continuous functions (in the topological sense), completeness and compactness. Covering pp. 229-266 in Lebl’s Basic Analysis I: Introduction to Real Analysis, vol. 1 (available as a free PDF download at https://www.jirka.org/ra/).

Prerequisites/Audience: 18.100A/P is the recommended prerequisite for this class. (18.100B/Q will have covered the material in this class.) Intended to bridge the gap between 18.100A and 18.100B for students with a basic understanding of material covered in 18.100A, ideally making further classes such as 18.101, 18.102, 18.103, 18.901 more accessible.

## Non-credit activities and classes:

### Math Lecture Series (non-credit version)

The same ten lectures listed above for 18.095 are also open to the public and you may attend as many or as few as you wish. Check back often to see new postings, including lecturers, titles and abstracts.

(Students wishing to receive course credit must register for 18.095, attend all ten lectures plus weekly recitations, and complete problem sets.)

### Modern Zero Knowledge Cryptography

- Ying Tong Lai, Yufei Zhao, Brian Gu, Jason Morton, Aayush Gupta, and Vivek Bhupatiraju
- Jan 11 - Feb 3 (MWF)

**With the exception of MLK Day 1/16, which will be held on Tuesday, 1/17.* - 2:00 - 3:30PM
- 4-237
**Office Hours:**2-136, Tuesdays 10AM - 12PM and Thursdays 5PM - 7PM.

The Modern Zero Knowledge Cryptography IAP program surveys recent advancements in ZK crypto over the last ten years, with a strong emphasis on their practical and user-facing applications. Topics covered range from the mathematical foundations of modern ZK protocols (elliptic curve cryptography, pairing-based cryptography, polynomial commitment schemes, zkSNARKs, etc.) to practical constructions of digital systems enabled by ZK primitives (digital identity, zero-knowledge machine learning, decentralized games, and more). Students will build their own ZK crypto project, with support from course staff and mentors.

For more details—course information, syllabus, sample projects, and more—visit https://zkiap.com/.

### Introduction to LaTeX

Enrollment: Unlimited, but sign-up required to have Canvas access (sign up at https://forms.gle/mik3BQ3teYxaabC37)

This will be an introduction to LaTeX, the programming language used for writing math (and other equation-dense) papers. Students learn basic codes, packages, and formatting they will need for writing papers in Course 18 CI-Ms, including 18.100P/Q, 18.200, 18.821. This self-paced, asynchronous workshop is geared for Course 18 majors, but might also be of interest to other equation-dense fields like Course 8 or Course 6. Asynchronous session.

Contact: Malcah Effron, (617) 324-2302,

### Integration Bee

Like solving integrals? Like watching other people solve integrals? Come try your problem solving skills against some of the best at the 42nd Annual MIT Integration Bee! Compete for the chance to win prizes and the prestigious title of Grand Integrator! To qualify for the bee, you must be a student and come to 4-149 for a 20-minute written test any time between 4pm and 6pm on Tuesday, January 24th. The top participants will be invited to the main event, which will be held on Thursday, January 26th at 6:00pm in 26-100. Come try out, and invite your friends to watch the finale! Whether you pass the qualifier or not, come watch your classmates show off their mad integrating skills at the main event will be held on Thursday, January 26th at 6:00pm in 26-100. Bring your friends!

For those of you who are not on campus or otherwise unable to come in-person, we have some good news! For the first time in Integration Bee history, the event will be live-streamed at https://web.mit.edu/webcast/math/iap23/

#### Qualifying Rounds (Open to participants only)

- Tuesday, January 24th
- 4:00pm-6:00pm
- 4-149

#### Finals (Open to the public)

- Thursday, January 26th
- 6:00pm-10:00pm
- Room 26-100

### Music Recital

- Thursday, January 26th
- 2:00PM
- Killian Hall

The MIT math department music recital will be returning once again this IAP, taking place in Killian Hall on 1/26/2022 starting at 2PM. The recital is a yearly tradition where we gather to listen to music performed by members of the math department. All styles of music are encouraged. Classical (Indian and western), jazz, video game, Latin-American, and Scandinavian folk music, as well as original compositions have all previously been featured.

Those interested in performing in the recital should contact Davis Evans at on or before January 23^{rd}.