Intro Math for Computer Science

Robinson Center for Young Scholars | Summer 2022

This course provides a transition from standard high school mathematics to the formal logic and discrete structures required for Computer Science. We focus on the language of proofs, the mechanics of sets, and the efficiency of algorithms.

1. Logic & The Language of Proofs

Before computing, we must define truth. This section covers tautologies, predicates, and the critical skill of negating quantified statements.

Notes Predicates & Quantifiers Introduction to universal and existential statements.
Quiz Logic & Negation Quiz Formalizing English sentences into logic.

2. Sets, Functions & Sequences

The building blocks of data structures. We explore function composition, cardinality, and the power of generating functions.

Worksheet Set Theory & Function Mapping
Worksheet Mathematical Thinking: non-commutativity
Quiz Function Injections & Bijections
Worksheet Generating Functions Solving recurrences using power series.

3. Induction & Complexity

How do we prove a program works for all inputs? And how long will it take to run?

Quiz Mathematical Induction Proving inequalities and sequence bounds.
Notes Algorithm Run-Time Complexity Big-O analysis for Arrays vs. Linked Lists.

4. The Final Project

Students chose a topic to investigate deeply, ranging from number theory to game implementation in Python.

Ideas Final Project Prompt A list of 10+ research and programming topics.