by Zach MC CLENEY

This semester, select students from Dalton and the Main School Bridging program who have interest and/or ability in higher level mathematics are taking Differential Equations HL an independent study and project centered course. Instead of learning a specific subject in mathematics students are are being exposed to higher level mathematics from linear algebra, complex variables, differential equations, probability, and more. All of these subjects are used in fields such as pure mathematics, physics, and engineering and are provided by the MIT open courseware (https://ocw.mit.edu/courses/mathematics/). There are four subjects of study;

**Complex Variables with Applications**: Complex analysis is a basic tool with a great many practical applications to the solution of physical problems. It revolves around complex analytic functions – functions that have a complex derivative. Unlike calculus using real variables, the mere existence of a complex derivative has strong implications for the properties of the function. Applications reviewed in this class include harmonic functions, two dimensional fluid flow, easy methods for computing (seemingly) hard integrals, Laplace transforms, and Fourier transforms with applications to engineering and physics.

Team Member: Danny, Kevin, Maxwell

**Linear Algebra**: This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.

Team Member: Michael, Claire, Eric, Teven

**Principles of Discrete Applied Mathematics**: This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes.

Team Member: Brian, Rice, Zoey, Elena, Alice

**Matrix Methods in Data Analysis, Signal Processing, and Machine Learning**: Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.

Team Member: Peter, Ben

During the course, students will use whatever resources the MIT courses provides (textbook, video lectures, reading assignments, etc.) to learn and practice the mathematics knowledge and skills needed in their subject. At least once every two weeks, each group must meet with their teacher to show their progress by explaining the concepts they recently studied and submit some sample work to be checked. To complete the course, each group will give a presentation to the class giving a summary of their subject, why it is important, and careers/research areas that use it.

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