Description of Course:
This course aims to introduce the basic concepts in topology and geometry that are essential for better understanding the ideas in theoretical physics. Some topics introduced in this course are maps and vector spaces, groups, topological spaces and topological invariants such as Euler characteristics, homotopy, homology, and deRham cohomology, and Lie groups as well as how they are connected to general relativity, quantum mechanics, electrodynamics, quantum field theory, and more. Through this course, we hope to build a bridge between mathematical and physical concepts for those who are interested in studying theoretical physics or who are curious about topology and geometry and how they are connected to physics. In this course, we would also provide resources to those who are interested in learning more about those topics.

Student Learning Objectives:
-Learn the Basic Concepts in Topology & Geometry
-Calculate Some Simple Examples to Further Understanding of the Concepts
-Have Ideas of How Those Mathematical Concepts are Connected to Physics
-Recognize Ways and Resources of Exploring Concepts Beyond this Course

Gradings:
-Attendance & Participation--25%
-Homework--25%
-Quiz 1--10%
-Quiz 2--10%
-Final Project--30%
A cumulative grade of 65% or above and a final project submission is required to pass the class.

Textbooks:
-Primary Textbook:
1. Mikio Nakahara. Geometry, Topology, and Physics.

-Other Textbooks:
1. Marian Fecko. Differential Geometry and Lie Groups for Physicists.
2. Kai S Lam. Topics in Contemporary Mathematical Physics.
3. Frederic Schuller. “Note for The WE-Heraeus international Winter School on Gravity and Light,” https://docs.wixstatic.com/ugd/6b203f_dc24fe06fbe14a71ae32a1ad031e1928.pdf?index=true.
4. Howard Georgi. Lie Algebras in Particle Physics.

Attendance & Participation:
Attendance and participation are 25% of the grade. You can make up absences with active participation, reading questions & summary, and/or extra credits from the homework.

Assignments:
Two Homework of Lowest Scores Will be Dropped.
Homework will be graded by completion.

Final Project:
Choose a topic related to the topics above and write a 2-page minimum expository or make a 10-minute presentation. Feel free to talk to us anytime if you have any questions regarding the final project and if you need any help with choosing and researching on the topic.

The logistics may undergo minor adjustments to optimize learning and adapt to the class's performance.

The class is first come, first served. However, this is challenging DeCal such that the prerequisites are -Calculus, Math 53, Math 54/Physics 89 or equivalent; -Physics 5A/B/C or 7A/B/C or equivalent; -Physics 137A is strongly recommended. We do not strictly enforce prerequisites, as mastery of the content can be achieved through various means beyond just attending the specified classes. This might include self-study through textbooks and papers, online courses, more advanced coursework, reading programs, etc. However, if we find you significantly lacking in the knowledge covered by these prerequisites, we suggest postponing your enrollment in this DeCal. Meanwhile, if you are a Math student who knows some of those math topics already and is interested in their applications in Physics. You are also welcome to take this DeCal. However, we are likely not to include rigorous proofs, unlike most math classes do.