Foundations of Mathematics and Computing

Department: 
MATH
Course Number: 
2740
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every Spring Semester (CS teaches in Fall)

This course introduces the essential mathematical concepts and computational techniques that form the basis of modern computing. The course emphasizes problem-solving, mathematical reasoning, and connections between mathematics and computing, preparing students for advanced study in theoretical and applied areas. This course is required for all concentrations in the Mathematics and Computing major.

 

MATH 2740 is crosslisted with CS 2740. 

MATH 2740 and MATH 2106 are mutually exclusive for credit: no student may hold credit for both courses. 

Prerequisites: 

(Math 1552 or Math 1X52 ) and (MATH 1553 or MATH 1554 or MATH 1X54 or MATH 1564)

Course Text: 

The course is based on lecture notes that draw from collections of different books or research papers. Here are a few references: 

 

  • Book of Proof (3rd edition), by Richard Hammack. 

  • Abstract Algebra: Theory and Applications (2019 edition), by Thomas Judson. 

  • Elementary Analysis: The Theory of Calculus, by Kenneth Ros. 

  • Introduction to Probability Models, by Sheldon M. Ross. 

  • Algorithms Illuminated Part I: The Basics, by Tim Roughgarden. 

  • Foundations of Machine Learning, Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar MIT Press, Second Edition, 2018. 

Topic Outline: 

  • Fundamentals of mathematical abstraction: sets, functions, and logic; 

  • Proof techniques: direct, contrapositive, existence, contradiction, and induction; 

  • Mathematical modeling by algebraic, differential, integral equations and optimization; 

  • Combinatorial structures: graphs, set systems, permutations,  

  • Mathematical description and analysis of algorithms; asymptotic analysis 

  • Combinatorics, counting, and probability 

  • Computer simulations of mathematical models; 

  • Introduction to machine learning and neural networks.