Real Analysis
A friendly introduction to real analysis.
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.
Official Enrollment Opens September 2023
This course is for students who want to pursue higher studies in mathematics, machine learning, engineering, or economics. It is also ideal for anyone with a genuine interest in mathematics that wants to deepen their understanding.
Improve mathematical problem-solving skills
Formally analyze limits, sequences and series
Identify and prove properties hold for functions
Understand why derivative and integral results in calculus work
Course Overview
Practice Quiz
Notation
Induction
Assignment: Induction
Archimedean Property
Quiz: Archimedean Property
Infimums + Supremums
Rationals and Density
Office Hours
Metric Spaces
Quiz: Metrics
Open and Closed Sets
Quiz: Open and Closed Sets
Assignment: Open and Closed Sets
Compact Sets
Quiz: Compact Sets
Survey: Topology
Midterm Exam 1
Intro to Sequences and Limits
Algebraic Properties of Limits
Cauchy Sequences
Divergent Sequences
Monotone Sequences
Subsequences
Liminf and Limsup
Series and Convergence Tests
Limits of Functions
Quiz: Limits of Functions
Continuous Functions
Assigment: Continuous Functions
Intermediate Value Theorem
Extreme Value Theorem
Uniform Continuity
Midterm Exam 2
Lesson - Derivative Definition
Lesson - Mean Value Theorem
Lesson - Riemann Integral
Lesson - Darboux Sums
Final Exam
Perfect
Perfect
Read LessWe 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.
Yes! This is precisely our goal, to help students better understand the concepts and how to apply them. We expect many students to be simultaneously enrolled in university courses (e.g. MATH 131A at UCLA).
Course memberships are $39/month for the course content; the ability to join Zoom office hours usually costs $30/month. However, current beta users have early access to Typal Academy while content is still undergoing much growth. To remedy any gaps in lesson plans, all beta students are welcome to join office hours with their membership.
Real analysis concepts are typically geometric in nature, and seeing canonical examples can go a long ways in developing intuition. Real analysis textbooks often either do not contain diagrams or very few (that are of low quality).
Not at all! We aim to empower aspiring scholars to learn effectively without forking out money to expensive universities. Some members even find this resource useful for preparing to go back to school for a graduate degree.
Each lesson includes key definitions and theorems along with several walkthrough examples that include both proofs and illustrative diagrams. These no-fluff lessons are written with a lighter tone than most textbooks, with sidebars from instructors giving intuition for the examples. Some lessons also include video mini-lectures.
The content for this course is typically studied over the course of 10 weeks. Yet, you can adjust that timeline as needed to suit your needs.
Access to the course contents costs $39 per month. All current users (i.e. beta users) can also attend weekly office hours with Eric on Sunday evenings.
Each lesson and quiz has an associated discussion tab where you are welcome to ask clarifying questions to the community. We update lessons to better clarify material based on community comments. You are also welcome to ask for more examples on a particular topic!
Nope! The content in our online course is self-contained. If you also want to complement your analysis studies with a textbook, we certainly encourage this!