MATH 1610 — Honors Calculus I

Lecture 1 (August 28, 2026): Introduction to the course and the language of set theory

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Lecture 2 (August 31, 2026): Set identities, paradoxes, and axioms for numbers

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Lecture 3 (September 4, 2026): Complete ordered fields and square roots

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Lecture 4 (September 11, 2026): Floors, density, and Dedekind cuts

The extended notes (beyond what we actually covered in lecture) additionally cover the digression on complex numbers and quaternions, and the beginning of our discussion of functions, area, and the integral.

lecture notes extended notes

Lecture 5 (September 18, 2026): Area, step functions, and the definite integral (with a hypercomplex number prelude)

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Lecture 6 (September 21, 2026): Properties of the integral, and the definition of a limit

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Lecture 7 (October 5, 2026): Limit laws, continuity, and the intermediate value theorem

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Lecture 8 (October 9, 2026): The intermediate value theorem and friends

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Lecture 9 (October 12, 2026): Uniform continuity, integrability of continuous functions, and the derivative

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Lecture 10 (October 16, 2026): The rules of differentiation

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Lecture 11 (October 19, 2026): Extrema, the mean value theorem, and the fundamental theorem of calculus

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Lecture 12 (October 23, 2026): Vectors, the dot product, Cauchy-Schwarz, and limits of vector-valued functions

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