Beta Enrollment Now Open

Some lessons are pending completion; however, we are creating and adding new content every week. Beta students have access to tutoring during weekly Zoom office hours.


Our real analysis course is for students who want to pursue higher studies in mathematics, machine learning, physics or statistics.

  • Improve mathematical problem-solving skills

  • Formally analyze limits, sequences and series

  • Understand why derivative and integral results in calculus work

Course Outline

    1. Course Overview

    2. Practice Quiz

    3. Notation

    4. Induction

    5. Assignment: Induction

    6. Archimedean Property

    7. Quiz: Archimedean Property

    8. Infimums + Supremums

    9. Assignment: Infimums + Supremums

    10. Rationals and Density

    11. Office Hours

    1. Metric Spaces

    2. Quiz: Metrics

    3. Open and Closed Sets

    4. Quiz: Open and Closed Sets

    5. Assignment: Open and Closed Sets

    6. Compact Sets and Connected Sets

    7. Quiz: Compact Sets

    8. Survey: Topology

    9. Midterm Exam 1

    1. Intro to Sequences and Limits

    2. Properties of Limits

    3. Cauchy Sequences

    4. Divergent Sequences

    5. Monotone Sequences

    6. Subsequences

    7. Liminf and Limsup

    8. Series and Convergence Tests

    1. Limits of Functions

    2. Quiz: Limits of Functions

    3. Assignment: Function Limits

    4. Continuous Functions

    5. Assigment: Continuous Functions

    6. Intermediate Value Theorem

    7. Assignment: Intermediate Value Theorem

    8. Continuous Functions + Compact Sets

    9. Assignment: Continuous Functions + Compact Sets

    10. Survey: Continuity

    11. Midterm Exam 2

    1. Lesson - Derivative Definition

    2. Lesson - Mean Value Theorem

    1. Lesson - Riemann Integral

    2. Lesson - Darboux Sums

    3. Final Exam

Course Highlights

  • Lessons for each major topic
  • Graphics for example proofs
  • Ability to ask questions

Analysis Taught via Graphics

Abstract definitions and theorems can be hard to digest. Our course makes concepts concrete by visualizing definitions and proof arguments.

Focus on Proof Techniques

Analysis courses usually focus on key theorems and too often leave details "as an exercise for the reader." However, students often experience the most headache in how to write proofs for homework and exams. Thus, we focus on supplying students with high-level outlines and walk-through proof examples.

Why Typal Academy?

We are unique in focusing our lessons on showing you how to write clear proofs and how to reason about each concept with intuitive diagrams. See below for how our course compares to alternatives.

Meet Your Instructors

Eric Erdős

Founder / Instructor

Our founder Eric loves learning and sharing new ideas. He has degrees in computer science, math, and physics. Eric spent several years tutoring and teaching for many STEM courses both through university and privately, including teaching in the math department at UCLA. During off time, he loves running and surfing.

Daisy Dirac


Daisy brings the cheerful spirit to the team. She applies the same gentle and warm teaching style as a mother reading children's books. In her off time, Daisy enjoys exploring coffee shops and practicing yoga and pilates.

Student Reviews

5 star rating


Yan Yang



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