Discrete Structures Notes (CIS*2910)

Comprehensive notes for Discrete Structures, written in Obsidian.

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Table of Contents

1️ Sequences

• Sequences
• Summation Notation

2️ Number Theory

• Number Theory

3️ Counting

• Counting

4️ Permutations & Combinations

• Binomial Theorem

5️ Mathematical Induction

• Practice Midterm

6️ Probability

• Discrete Probability

7️ Graph Theory

• Graph Theory

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Quick Reference

Key Formulas

Sequences:

• Geometric: $a, ar, ar^2, \ldots, ar^n$
• Arithmetic: $a, a+d, a+2d, \ldots, a+nd$

Summation: $$\sum_{j=m}^{n} a_j = a_m + a_{m+1} + \cdots + a_n$$

Combinations: $$\binom{n}{r} = \frac{n!}{r!(n-r)!}$$

Binomial Theorem: $$(x+y)^n = \sum_{j=0}^{n} \binom{n}{j}x^{n-j}y^j$$

Probability: $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$

Handshake Lemma: $$2m = \sum_{v \in V} \deg(v)$$

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Contributing

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Course Information

Course: CIS 2910 - Discrete Structures
Topics Covered:

• Sequences & Summations
• Number Theory & Modular Arithmetic
• Counting Principles
• Combinatorics
• Probability Theory
• Graph Theory

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Last updated: [April 14th, 2026]

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