MAT 616 information
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Course Title:
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ELEMENTS OF MATHEMATICS, PROGRAMMING AND COMPUTER SCIENCE FOR DATA SCIENCE
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Institution:
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Buffalo State University
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Format:
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Lecture + Python Lab
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Course Description
This course introduces the mathematical foundations needed to understand modern Data Science and Machine Learning. Emphasis is placed on interpretation, geometry, probability, and optimization rather than formal proof. Mathematics is presented as a modeling language for data-driven reasoning.
Learning Outcomes
By the end of this course, students will be able to:
- Interpret machine learning algorithms mathematically
- Connect data representations to geometric and probabilistic ideas
- Understand optimization as the mechanism of learning
- Translate mathematical ideas into working Python code
- Critically evaluate assumptions and limitations of models
Assessments
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Component
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Weight
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Weekly Python Labs
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40%
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Concept Checks (Low-stakes quizzes)
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15%
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Midterm Concept Synthesis
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15%
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Final Project (Math → ML Explanation)
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30%
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Schedule
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Module
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Topics
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1
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Mathematical Modeling & Data
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2
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Functions, Graphs, and Transformations
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3
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Vectors & Geometry of Data
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4
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Matrices as Operators
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5
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Linear Models & Least Squares
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6
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Probability Foundations
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7
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Statistics & Sampling
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8
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Optimization & Loss Functions
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9
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Derivatives as Sensitivity
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10
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Multivariate Learning & Backpropagation
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11
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Dimensionality Reduction (PCA)
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12
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Modern Machine Learning & Limits
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Course Design Philosophy
Mixed Mathematical Backgrounds
This course assumes no prior calculus or linear algebra. Mathematical ideas are introduced through:
- Visualization
- Geometry
- Numerical experimentation
- Code-first exploration
Calculus Policy
- Derivatives are introduced as sensitivity
- Gradients as direction of improvement
- No symbolic differentiation required
- Numerical gradients used first
Support Structures
- Optional Math Refresh notebooks
- Peer collaboration encouraged
- Multiple explanation modalities allowed (text, code, diagrams)
Program Alignment
This course supports:
- Data Science & Analytics programs
- Computer Science programs
- Applied Mathematics pathways
- Interdisciplinary AI curricula
Preparation for Advanced Topics
Students completing this course are prepared for:
- Machine Learning
- Deep Learning
- Statistical Learning
- AI Ethics & Model Evaluation
