Applied Finite Mathematics — Complete Study Guide | Shelemu Tesfaye
APPLIED FINITE
MATHEMATICS
Complete Study Guide & Exam Preparation Notes
Harvard University
Business • Economics • Computer Science • Social Sciences
Author: Shelemu Tesfaye
Academic Year 2025 – 2026
Covering 10 Chapters | 150+ Worked Examples | Mock
Exam
Chapters: Sets & Logic • Matrices • Linear Programming • Finance • Probability
Counting • Statistics • Markov Chains • Game Theory • Mock Examination
Harvard University • Business & Applied Mathematics Page #
,Applied Finite Mathematics — Complete Study Guide | Shelemu Tesfaye
Course Description
Applied Finite Mathematics focuses on mathematical techniques used in business, economics,
computer science, social sciences, and decision-making. This study guide provides clear
explanations, worked examples, formulas, practice questions, and exam preparation materials
designed to help students master key concepts in finite mathematics.
Learning Outcomes
• Solve finite mathematics problems using logical and quantitative methods
• Apply matrix techniques to model and solve real-world business situations
• Analyze probability and statistical data to make informed decisions
• Use mathematical models for business optimization and forecasting
• Understand financial mathematics including interest, annuities, and present value
• Apply counting principles, Markov chains, and game theory to applied problems
Harvard University • Business & Applied Mathematics Page #
, Applied Finite Mathematics — Complete Study Guide | Shelemu Tesfaye
Chapter 1: Introduction to Finite Mathematics
1.1 What is Finite Mathematics?
Finite Mathematics is a branch of mathematics that studies mathematical structures, systems,
and processes that are discrete (finite) in nature. Unlike calculus, which deals with continuous
change, finite mathematics operates on distinct, countable values. It provides the analytical
tools used across business, economics, computer science, and the social sciences.
1.2 Core Application Domains
• Business & Economics: Optimization of costs, profits, resource allocation, and financial
modeling
• Computer Science: Algorithm design, logic circuits, database theory, and network
analysis
• Social Sciences: Survey analysis, voting models, probability in sociological studies
• Decision Science: Game theory, Markov chains, decision trees
1.3 Mathematical Modeling
A mathematical model is an abstract representation of a real-world problem expressed using
mathematical language. The steps in modeling are:
1. Identify the problem and define variables
2. Translate relationships into mathematical equations or inequalities
3. Solve the mathematical problem using appropriate techniques
4. Interpret the solution in the context of the original problem
5. Validate the model against real data
WORKED EXAMPLE
A company produces x units of product A and y units of product B. If each unit of A earns $5
profit and B earns $8, express total profit P as a function.
Solution: P(x, y) = 5x + 8y. This is a linear objective function in two variables, commonly
used in linear programming.
Harvard University • Business & Applied Mathematics Page #
APPLIED FINITE
MATHEMATICS
Complete Study Guide & Exam Preparation Notes
Harvard University
Business • Economics • Computer Science • Social Sciences
Author: Shelemu Tesfaye
Academic Year 2025 – 2026
Covering 10 Chapters | 150+ Worked Examples | Mock
Exam
Chapters: Sets & Logic • Matrices • Linear Programming • Finance • Probability
Counting • Statistics • Markov Chains • Game Theory • Mock Examination
Harvard University • Business & Applied Mathematics Page #
,Applied Finite Mathematics — Complete Study Guide | Shelemu Tesfaye
Course Description
Applied Finite Mathematics focuses on mathematical techniques used in business, economics,
computer science, social sciences, and decision-making. This study guide provides clear
explanations, worked examples, formulas, practice questions, and exam preparation materials
designed to help students master key concepts in finite mathematics.
Learning Outcomes
• Solve finite mathematics problems using logical and quantitative methods
• Apply matrix techniques to model and solve real-world business situations
• Analyze probability and statistical data to make informed decisions
• Use mathematical models for business optimization and forecasting
• Understand financial mathematics including interest, annuities, and present value
• Apply counting principles, Markov chains, and game theory to applied problems
Harvard University • Business & Applied Mathematics Page #
, Applied Finite Mathematics — Complete Study Guide | Shelemu Tesfaye
Chapter 1: Introduction to Finite Mathematics
1.1 What is Finite Mathematics?
Finite Mathematics is a branch of mathematics that studies mathematical structures, systems,
and processes that are discrete (finite) in nature. Unlike calculus, which deals with continuous
change, finite mathematics operates on distinct, countable values. It provides the analytical
tools used across business, economics, computer science, and the social sciences.
1.2 Core Application Domains
• Business & Economics: Optimization of costs, profits, resource allocation, and financial
modeling
• Computer Science: Algorithm design, logic circuits, database theory, and network
analysis
• Social Sciences: Survey analysis, voting models, probability in sociological studies
• Decision Science: Game theory, Markov chains, decision trees
1.3 Mathematical Modeling
A mathematical model is an abstract representation of a real-world problem expressed using
mathematical language. The steps in modeling are:
1. Identify the problem and define variables
2. Translate relationships into mathematical equations or inequalities
3. Solve the mathematical problem using appropriate techniques
4. Interpret the solution in the context of the original problem
5. Validate the model against real data
WORKED EXAMPLE
A company produces x units of product A and y units of product B. If each unit of A earns $5
profit and B earns $8, express total profit P as a function.
Solution: P(x, y) = 5x + 8y. This is a linear objective function in two variables, commonly
used in linear programming.
Harvard University • Business & Applied Mathematics Page #
