Mathematics for Computer Science

As taught in: Fall 2005

Level:

Undergraduate

Instructors:

Prof. Albert Meyer

Prof. Ronitt Rubinfeld

Course Features

Course Highlights

Course Description

Course logo. (Image courtesy of Nick Matsakis.)

Course Features

• Lecture notes
• Assignments and solutions
• Exams and Solutions

Course Highlights

This course features a full set of lecture slides, assignments and course notes in the readings section.

Course Description

This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineering. The course divides roughly into thirds:

1. Fundamental Concepts of Mathematics: Definitions, Proofs, Sets, Functions, Relations
2. Discrete Structures: Modular Arithmetic, Graphs, State Machines, Counting
3. Discrete Probability Theory

A version of this course from a previous term was also taught as part of theSingapore-MIT Alliance (SMA) programme as course number SMA 5512 (Mathematics for Computer Science).

Lecture Notes

Powerpoint and LaTeX source files and LaTeX macros are available to instructors by request: email Prof. Albert Meyer at meyer at csail dot mit dot edu.

LEC #	TOPICS	LECTURE NOTES
1	Course Overview Single Particle Dynamics: Linear and Angular Momentum Principles, Work-energy Principle	(PDF)
2	Examples of Single Particle Dynamics	(PDF)
3	Examples of Single Particle Dynamics (cont.)	(PDF)
4	Dynamics of Systems of Particles: Linear and Angular Momentum Principles, Work-energy Principle	(PDF)
5	Dynamics of Systems of Particles (cont.): Examples Rigid Bodies: Degrees of Freedom	(PDF)
6	Translation and Rotation of Rigid Bodies Existence of Angular Velocity Vector	(PDF)
7	Linear Superposition of Angular Velocities Angular Velocity in 2D Differentiation in Rotating Frames	(PDF)
8	Linear and Angular Momentum Principle for Rigid Bodies	(PDF)
9	Work-energy Principle for Rigid Bodies	(PDF)
10	Examples for Lecture 8 Topics	(PDF)
11	Examples for Lecture 9 Topics	(PDF)
12	Gyroscopes: Euler Angles, Spinning Top, Poinsot Plane, Energy Ellipsoid Linear Stability of Stationary Gyroscope Motion	(PDF)
13	Generalized Coordinates, Constraints, Virtual Displacements	(PDF)
14	Exam 1
15	Generalized Coordinates, Constraints, Virtual Displacements (cont.)	(PDF)
16	Virtual Work, Generalized Force, Conservative Forces Examples	(PDF)
17	D'Alembert's Principle Extended Hamilton's Principle Principle of Least Action	(PDF)
18	Examples for Session 16 Topics Lagrange's Equation of Motion	(PDF)
19	Examples for Session 17 Topics	(PDF)
20	Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange's Equation for Nonholonomic Systems, Examples	(PDF)
21	Stability of Conservative Systems Dirichlet's Theorem Example	(PDF)
22	Linearized Equations of Motion Near Equilibria of Holonomic Systems	(PDF)
23	Linearized Equations of Motion for Conservative Systems Stability Normal Modes Mode Shapes Natural Frequencies	(PDF)
24	Example for Session 23 Topics Orthogonality of Modes Shapes Principal Coordinates	(PDF)
25	Damped and Forced Vibrations Near Equilibria	(PDF)
26	Exam 2