Why Calculus Works: A Beginner’s Tour of Real Analysis

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Why Calculus Works: A Beginner’s Tour of Real Analysis

SAT Score Range

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1 session

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This series ended on July 16, 2025. All 1:1 and group chats related to this series are disabled 7 days after the last session.

About

Have you ever wondered why the rules of calculus work the way they do? In this session, we’ll explore the foundational ideas of real analysis that give calculus its rigour and precision. We’ll introduce concepts like the epsilon delta definition of a limit, what it truly means for a function to be continuous, and how to begin thinking in proofs. This session is designed for students who have studied or are currently studying calculus and are curious about the "why" behind the formulas. No experience with proof-writing is required, just curiosity and a willingness to think more deeply about familiar ideas.

Tutored by

Anna P 🇬🇧

Certified in 11 topics

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I'm an Anglo-Saxon. I'm British and American. I'm a high-functioning autistic. I love trains. I love Our Lord Jesus Christ and Our Lady, the Blessed Virgin Mary. I like European history, computational biology, learning new languages, pure mathematics, physics, philosophy, and theology. I provide tutoring in Algebra II, Calculus, and Physics.

Schedule

✋ ATTENDANCE POLICY

If you sign up, please try your best to attend live or let me know ahead of time if you can’t make it. If you miss two sessions without notice, you may be removed from the series to make room for others.

SESSION 1

16

Jul

SESSION 1

Other Topics

Wed 4:15 AM - 5:15 AM UTCJul 16, 4:15 AM - 5:15 AM UTC

In this series, we’ll take a deeper look at the foundations of calculus through the lens of introductory real analysis. We’ll begin by understanding the real number system, including concepts like bounds, supremum and infimum, and why completeness matters. From there, we’ll build toward the formal ε δ definition of a limit, carefully unpacking what it means and how to apply it in simple proofs. We’ll then use this framework to define and explore continuity, examining functions that are continuous and those that are not, with intuitive and rigorous examples. If time permits, we may touch on the Intermediate Value Theorem, uniform continuity, and the idea of convergence of sequences and functions. Along the way, you’ll be introduced to proof-based mathematical thinking, including basic techniques like direct proofs and proof by contradiction, all in a supportive, beginner-friendly environment.

Public Discussion

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Jul 16

1 week

60 mins

/ session

SCHEDULE

Wednesday, Jul 16

4:15AM