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Enrichment • Series

An Introduction to Mathematical Analysis

Nathan J

Series Details

Sessions

Public Discussion

This series ended on April 1, 2023. All 1:1 and group chats related to this series are disabled 7 days after the last session.

Series Details

About

We will begin with ideas of Real Analysis, Topology, Differential Geometry, and continue to explore Complex Analysis and Partial Differential Equations. Depending on the progress of learners, we may explore the applications of these concepts to physics in General Relativity and QFT.

Tutor Qualifications

Relating to mathematics, I scored a 5 on the AP Calculus exam, and studied Calculus III, ODEs, and Linear Algebra during my 8th grade and I continue to learn the contents of Real Analysis, Complex Analysis, Modern Algebra, and PDEs through a Stanford online program. I find the topics of mathematics interesting in and of themselves as logical principles and by virtue of their ready applications to Physics and Chemistry in pursuit of an objectively transcendent form of the truth which underlies what we know as reality.

✋ ATTENDANCE POLICY

Try to attend all session as the implementation of each session is contingent on previous content. Prerequisites include Calculus I,II, III, Ordinary Differential Equations, Linear Algebra, Number Theory, and experience with formal mathematical proof.

Dates

March 4 - April 1

Learners

7 / 10

Total Sessions

8

About the Tutor

I'm currently a high school student in Missouri. As some background, during my eighth grade year, I took Calculus I, II, and III, followed by AP Physics C and AP Chemistry during my freshman year and scored a 5 in both examinations. I then self-studied Quantum Physics I, Quantum Physics II, Organic Chemistry General Relativity, and some of Quantum Physics III on MIT Opencourseware and Khan Academy. Along with this I took Real Analysis, Linear Algebra, Complex Analysis, Modern Physics, and Number Theory through a Stanford online program, and I continue to pursue QFT, General Relativity, and Partial Differential Equations. Through WashU, I’ve met Professor Thornton and Professor Rodsphon with whom I’ve discussed concepts in Analysis and Topology. Through the physics department, I’ve been researching Quantum Information with Professor Murch and Henriksen.

View Nathan J's Profile

Upcoming Sessions

0

Past Sessions

8
4
Mar

Session 1

Orientation

We will introduce ourselves and I will give a preliminary prompt for the course materials and topics. To begin, we will complete one of the MIT Integration bee problem sets, along with other engaging activities. I will also introduce available resources to further explore the subject matter.
5
Mar

Session 2

Even More Math

We will begin to explore the principles of Real Analysis and preview the use of Latex.
9
Mar

Session 3

Office Hours

We will begin to explore the principles of Real Analysis and preview the use of Latex.
11
Mar

Session 4

Even More Math

Mathematical proofs and an axiomatic preview of Real Analysis.
12
Mar

Session 5

Even More Math

Consequences of Axioms, "Infinity", formal limits, and associated theorems.
18
Mar

Session 6

Even More Math

Sequences, Series, and formal proof for the elementary properties of calculus.
25
Mar

Session 7

Even More Math

Review of Taylor Series, Lebesgue integration, and proof of further properties of calculus. We will begin reviewing the topics of Real Analysis holistically and discuss its implementations.
1
Apr

Session 8

Physics

Partial Differential Equations, General Relativity, Abstract Algebra, and a final review of past concepts.

Public Discussion

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