Research Courses

Welcome!

We are excited to celebrate the launch of SevenSphere with a

FREE first course

"Topology, Knot Theory, and Manifolds"

Limited to 8 students per section.

Space still available in the High School and Community Sections. Grab your spot today!

Instructor: Nathan Dowlin

BS Yale ‘11, PhD Princeton ‘16

10 years teaching experience

Princeton • Stanford • Columbia • Dartmouth

Topology, Knots, and Manifolds

Target Audience Meeting Times Location
High School Graduating Class Years 2025-2027 Mon. and Wed.
10:00am-11:30am PST
June 16 -- July 9		 In Person
Menlo Park
High School Graduating Class Years 2025-2027 Mon. and Wed.
1:00pm-2:30pm PST
June 16 -- July 9		 Virtual, Zoom
College Graduating Class Years 2027-2028 Tues. and Thurs.
1:00pm-2:30pm PST
June 17 -- July 10		 Virtual, Zoom
Community (Available to Everyone) Wednesday
3:00pm-4:30pm PST
June 18 -- August 6		 In Person
Menlo Park

Cost: $1000 Free (Inaugural class)

Start date: June 16, 2025

Registration Deadline: June 5, 2025

Topics: We will work to understand objects in various dimensions and the different tools that can be used to build these objects and analyze them. Specific topics include: Euler characteristic, cellular decompositions, genus of surfaces and knots, and the Jones and Alexander polynomials.

Numbers, Sets, and Infinity

Cost: $1000

Start date: July 14, 2025

Registration Deadline: July 1, 2025

Topics: We will study how numbers are constructed from the ground up, and some of the difficulties and paradoxes that arise as a result. Specific topics include: countable and uncountable infinity, sets vs collections, and Gödel's incompleteness theorems.

Target Audience
 Meeting Times Location
High School Graduating Class Years 2025-2027 MW 10:00am-11:30am PST July 14 -- August 6 In Person, Downtown Menlo Park
High School Graduating Class Years 2025-2027 MW 1:00pm-2:30pm PST July 14 -- August 6 Virtual, Zoom
College Graduating Class Years 2027-2028 TTh 1:00pm-2:30pm PST July 15 -- August 7 Virtual, Zoom
Community (Available to Everyone) Monday
7:30pm-9:00pm PST
July 14 -- Sept 1		 Virtual, Zoom

Fractal Geometry

Target Audience
 Meeting Times Location
High School Graduating Class Years 2025-2027 TBD In Person, Downtown Menlo Park
High School Graduating Class Years 2025-2027 TBD Virtual, Zoom
College Graduating Class Years 2027-2028 TBD Virtual, Zoom
Community (Available to Everyone) TBD In Person
Menlo Park

Cost: $1000

Start Date: September 2025 (date TBD)

Application Deadline: August 15, 2025

Topics: We will explore objects exhibiting self-similarity (like the Sierpinski Triangle shown here), and ways of defining and computing dimension of these objects. Specific topics include: box-counting dimension, the Moran equation, the Mandelbrot set, and Julia sets.

Student Reviews of the Instructor

  • “If Nathan Dowlin is teaching this class, then TAKE IT! Best professor I ever had.”

    – Stanford student

  • “Nate is possibly the best math teacher I’ve ever had. He’s easy to understand, cares so much about our learning, and teaches us a new appreciation for math.”

    – Princeton student

  • “He’s absolutely the best math professor/teacher I’ve ever had, makes the course interesting, even though Calc 2 can be really boring, always gives us riddles before or after class to get us thinking, is always able to explain something a different way if someone doesn’t understand it the first time, and he’s at the actual nicest human being on the planet. Sometimes math professors get so caught up in their own heads that they can’t figure out a way to explain the material to someone who [isn’t a math major / doesn’t think like a math professor / just doesn’t understand the first time around], but this is absolutely NOT the case for professor Dowlin. I could not give enough positive feedback for this guy!”

    – Columbia student

  • “I don't enjoy math as a subject but I felt very lucky to have Professor Dowlin as my teacher. He is great at explaining concepts and simplifying things that seem scary. Something that stood out to me was how he addressed us when we were really confused. I remember after the introduction to a tough topic he saw us all blank-faced and said ‘It's okay if you don't understand all of this, it's a tough one to grasp so don't worry’ and it made me feel much more secure in the course because it was clear he was empathetic towards his students and wanted us to succeed without being intimidated by math. Thanks for everything Professor Dowlin! I wish you luck in the future on your next endeavor beyond Dartmouth.”

    – Dartmouth student

  • “Professor Dowlin is an incredible professor! He's clear, always asks for questions, writes and speaks at the perfect pace, and goes methodically through the material. He's brilliant and yet can explain the material in a way anyone can understand. He teaches for students. He is also very approachable, which makes asking questions easy. Also, we all love his riddles! I would take any class he teaches.” 

    – Columbia student