100 free lessons · Worked examples and practice

Undergraduate math

Explore selected university topics across proof, algebra, geometry, analysis, and probability. Each lesson offers a focused entry point with an explicit problem and a worked argument you can reconstruct.

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Use the pictures and worked reasoning as a starting point. Make your own sketch, explain your choices, and check the result.

Your study guide

What you will explore.

Read and construct mathematical arguments
Connect algebraic, geometric, and analytic viewpoints
Apply models while checking their hypotheses

Before you begin

There is no single linear prerequisite chain across all 100 lessons. Choose a subject you know, read its prerequisites, and review the necessary calculus, linear algebra, or proof techniques first.

Review Grade 12

How to study these lessons

Rewrite the argument without looking at the solution. Identify where each assumption enters, and try a small example or counterexample to test the boundaries of the claim.

Work at your own pace. Open a hint when you need it, then try again before revealing the complete explanation.

Grade labels are starting-point guides; school sequences vary. University lessons introduce selected topics and assume the prerequisites listed on each page.

Practice with a moving example

650 guided practice chapters for Undergraduate.

Try a distinct question, open a hint, compare the worked solution, and explore its interactive animation. These scenario chapters give you more practice within this level’s topics.

Open the practice collection

Learn with Amar

Teaching videos, chapter by chapter.

Teaching recordings for this level are being prepared. Browse the chapter index to see video availability and open the written lessons that are ready now.

Browse chapters and video availability

Learn one idea at a time

Your Undergraduate lesson collection.

The lessons appear in their suggested study order. Choose the first lesson for a starting point, or use the search and subject filters to review a particular skill. Read the prerequisites whenever you change topics.