# IAP 2024 Classes

## For-credit subjects:

### 18.02A Calculus

- Prof Bill Minicozzi and staff
- Jan. 8 - Feb. 2
- 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 Melissa Sherman-Bennet
- Jan. 8-26
- MWF 11-1
- Classroom: 2-142

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 2-147.
**Website:**https://math.mit.edu/classes/18.095/2024IAP/

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 8 | Laurent Demanet | Compressed Sensing |

Wednesday, January 10 | Jeremy Kepner & Hayden Jananthan | Mathematics of Big Data & Machine Learning |

Friday, January 12 | Tristan Ozuch | Gauss' Theorema Egregium |

Wednesday, January 17 | TBA | |

Firday, January 19 | Peter Shor | Continued Fractions |

Monday, January 22 | Jon Kelner | Random Walks, Discrete Harmonic Functions, and Electrical Circuits |

Wednesday, January 24 | Keaton Burns | Numerical simulations with exponential accuracy |

Firday, January 26 | John Bush | Surface Tension |

Monday, January 29 | Roman Bezrukavnikov | TBA |

Wednesday, January 31 | Daniel Alvarez-Gavela | The Hairy Ball Theorem |

Friday, February 2 | Paul Seidel | Stokes phenomenon |

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

- Profs Alan Edelman and Steven Johnson
- Jan 16 - Feb 2
- MWF 11am-1pm
- This class will meet in 2-105.

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 and Przemysław Szufel
- Jan 16 - 19
- TWRF 11am-12:30; 1pm-3pm
- This class will meet in 2-132.

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 is like Python, in that it 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 scale your computations beyond a single computer.

This course does not require the participants to have prior detailed knowledge of advanced machine learning algorithms nor the Julia programming language. What we assume is a basic knowledge of data science tools (like Python or R) and techniques (like linear regression, basic statistics, plotting).

All course materials will be made available on a dedicated GitHub repository during the course.

Schedule

- Day 1 (Tuesday, Jan 16, 2024)
- 11:00-12:30 Your first steps with Julia
- 13:00-15:00 Working with tabular data

- Day 2 (Wednesday, Jan 17, 2024)
- 11:00-12:30 Classical predictive models
- 13:00-15:00 Advanced predictive models using machine learning

- Day 3 (Thursday, Jan 18, 2024)
- 11:00-12:30 Numerical methods
- 13:00-15:00 Solving optimization problems

- Day 4 (Friday, Jan 19, 2024)
- 11:00-12:30 Differential equations
- 13:00-15:00 Scaling computations using parallel computing

Location: Room 2-132 on MIT Campus. See http://whereis.mit.edu/?mapterms=2-132 for location.

Instructors: Michał Bernardelli, Łukasz Kraiński, Julian Samaroo, Przemysław Szufel, Bartosz Witkowski

**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

- Dr. Melissa Sherman-Bennett
- Jan 16 - Feb 2
- TR 11:00-12:30
- 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.

### 18.S191 Special Subject in Mathematics:

- Christopher Rackauckas
- Jan 9-Feb 2
- MWF11-12
- This class will meet in person on campus in room 2-135.

3 units (P/D/F-graded)

Title: Composable System Modeling and Its Compilation

Guest Lecturers: Yingbo Ma, Modeling and Numerics Team Lead, JuliaHub, Brad Carman, Engineering Manager, System Modeling, Instron

Traditionally, modeling physical systems often requires a deep understanding of the physics and equations of motions or states, simplifying the differential equations using conservation laws and constraints, and finally implementing simplified equations in a scientific computing language to numerically solve them. However, this workflow is tedious and not expressive. A simple change in the underlying physical system often requires a complete re-derivativation of the simplified equations. A composable modeling system frees domain experts from the time-consuming derivation, simplification, and implementation by allowing them to model each physical component separately and hierarchically, thereby enabling them to build more accurate and complex models without compromising the simulation performance. In this course, we will dive into the practice of implementing composable physical models and the compilation process of the model system using the ModelingToolkit.jl acausal modeling framework in Julia. Students will learn the mathematics and numerical methods behind solving industry-scale models, covering topics such as differential-algebraic equations (DAEs), modern techniques in implicit integrators (backwards differentiation formulae (BDFs)), symbolic manipulation of equations via techniques like Pantelides algorithm and tearing of nonlinear systems, and more. Applications for solving real-world problems like modeling battery systems of electric vehicles, efficient control of hydraulic and HVAC systems, and more will be used to demonstrate how these techniques are used in industrial settings.

## 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.)

### 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

**43rd Annual MIT Integration Bee**

- Bee:
**Wednesday**, January 24th, 2024, 6:30pm in 26-100 - Qualifier: Monday, January 22nd, 2024, 4-6pm (any 20-minute block) in 4-149
- Contact:
- Link: https://math.mit.edu/~yyao1/integrationbee.html

### Music Recital

Stay Tuned!!!