Quantitative Reasoning
This course introduces foundational concepts in discrete mathematics, probability, and predictive modeling, along with computational tools for analyzing data.
Instructor: Dipto Das
Term: Fall
Location: Remote (Zoom)
Time: Mondays and Wednesdays, 3:35–4:50 PM
Course Overview
This course introduces methods for quantitative reasoning about data. Students will:
- Learn logic, set theory, and foundational mathematical concepts
- Apply probability and statistical reasoning to real-world problems
- Use combinatorics and distributions to model uncertainty
- Develop computational skills using Python and Jupyter notebooks
- Build predictive models and interpret relationships in data
Prerequisites
- Introductory programming experience (Python recommended)
- Basic algebra
Textbooks
- No required textbook
- Supplementary materials and notes provided in class
Grading
- Quizzes: 10%
- Homework: 30%
- Exam 1: 20%
- Exam 2: 20%
- Final Exam: 20%
Schedule
| Week | Date | Topic | Materials |
|---|---|---|---|
| 1 | Course Overview and Motivation Introduction to quantitative reasoning, course structure, and tools (JupyterHub). | ||
| 2 | Logic and Reasoning Foundations of logical thinking and introduction to testing and LaTeX. | ||
| 3 | Sets and Functions Set theory, functions, and their role in reasoning about data. | ||
| 4 | Linear Algebra Foundations Scalars, vectors, and matrices for data representation. | ||
| 5 | Exam 1 Covers fundamentals of logic, sets, and linear algebra. | ||
| 6 | Descriptive Statistics and Distributions Introduction to statistics and probability distributions. | ||
| 7 | Conditional Probability Understanding dependent events and conditional reasoning. | ||
| 8 | Expected Value Calculating expectations and interpreting outcomes. | ||
| 9 | Bayes’ Rule Bayesian reasoning and updating beliefs with data. | ||
| 10 | Exam 2 Covers probability and statistical reasoning. | ||
| 11 | Combinatorics Permutations and combinations for counting problems. | ||
| 12 | Binomial Distribution Modeling discrete probability outcomes. | ||
| 13 | Normal Distribution Continuous distributions and statistical inference. | ||
| 14 | Regression and Correlation Modeling relationships between variables. | ||
| 15 | Final Exam Comprehensive final exam. |