Description: From models in quantitative finance and econometrics to function theory in mathematics to aviation to theories in physics to the study of epidemics and population dynamics, the role of Calculus in shaping our modern world could not be overstated.
Our “Calculus” or “How To Think: Calculus” series is a unique course that introduces the subject with its historical motivation, in a manner that is rigorous, clear and mathematically precise and points to applications of this miracle of mathematics in the modern world.
Through our unique blend of rigorous proof-based exposition and strong focus on problem-solving, we combine the best aspects of treatises on Calculus at both the school and university levels.
Our rigorous approach will help participants really understand what underlies the logic of calculus that’s often omitted at a school level, and our problem-solving approach will help them build competitive skills that will improve their ability to solve problems they may encounter in an exam setting or higher education.
Duration: 8 weeks (October 23 to December 25, 2025)
Format: Online 1-hour lectures, twice a week, in the style of lectures at Oxford and Cambridge.
Style: Focus on historic motivation, mathematical rigour and real-world applications of Calculus.
Homework: Assigned every week in advance of the classes.
Office Hours: Once every two weeks, after every four lectures, 1 hour of office hours to discuss solutions to all the homework problems in the previous two weeks.
Grades: Part I is best suited for students in grade 11, advanced students in grades 9 or 10, and students in grade 12 looking to revisiting the content in Part I of Calculus. Part II is best suited for students in grade 12 and advanced students in grades 10 or 11 comfortable with most of Part I content.
Part I — Best suited for grade 11 or advanced students in grades 9 or 10, and grade 12 students revisiting the content.
- Real Numbers
- Sets and Function Theory
- Sequences and Series
- Convergence and Divergence
- Limits and Continuity
- Derivatives and Differentiation
- Derivative Toolkit and Proofs
- Applications of Derivatives
Part II — Best suited for grade 12 or advanced students in grades 10 or 11 comfortable with a chunk of Part I content.
- Sets and Function Theory
- Limits and Continuity
- Mean Value Theorems
- Integrals and Integration
- Integration Toolkit and Techniques with Proofs
- Applications of Integration to the Modern World
- Differential Equations
- Areas, Volumes and Parametric Curves
- Change of Coordinates and Multivariate Integration
- Special Tricks in Integration