# CS 4850

## Mathematical Foundations for the Information Age

Location: Gates Hall G01

Lecture: MWF 1:25pm - 2:15pm

Instructor: John Hopcroft

Office Hours: By Appointment

Textbook (2018): Mathematical Foundations for the Information Age

## Announcements

**1/29**: Due to room restrictions, Joshua Hull's Office Hours on Saturday, February 3rd will take place in Rhodes 412

**1/28**: Due to instructor travel, the lecture on Monday, February 5th will be covered by Eric Hans Lee and will mainly consist of chapter 2 review followed by a quick preview of the next section

**1/14**: IMPORTANT: The first class will take place on Friday, January 26th instead of Wednesday, January 24th due to instructor travel

## Concepts

This course will focus not only on Discrete Math, but also Probability Theory and Numerical Methods. In this light, materials covered in **CS 2800: Discrete Structures**, **MATH 1910: Calculus for Engineers** or **MATH 1920: Multivariable Calculus for Engineers**, and **MATH 2210: Linear Algebra** or **MATH 2940: Linear Algebra for Engineers** are recommended prerequisites for the course. Students with a particular weakness in one of these areas are highly encouraged to come to office hours or request tutoring early on.

We will cover the mathematical foundations of data science, machine learning, and other mathematically-intensive areas of Computer Science. A sparse sampling of fundamental concepts includes High-Dimensional Spaces, the Singular Value Decomposition, Random Walks, Machine Learning, Massive Data, Clustering, and Topic Models. For a complete list of concepts covered in this course, please see the textbook's table of contents. We hope to cover most, if not all, of the material in the textbook by the end of this semester.

The textbook used in this class is **Mathematics for the Information Age by Avrim Blum, John Hopcroft and Ravindran Kannan **. The 2018 edition of the book can be accessed here. There are many different editions of the book online which may have different numbers for the chapter questions. Please refer to this most recent edition for correct HW questions.

Your grade will be roughly calculated as follows: ** 40% HW, 60% Exams**. However, note that this is simply a rough estimate; we plan to grade holistically. For example, if a student does poorly on the first midterm, but brings his/her later grades up, we will give the later test scores more weight as this shows hard work on the student's part.

## Exams

Midterms will taken in-class

- Midterm 1: 3/2

- Midterm 2: 3/28

- Midterm 3: 4/27

** Exam Regrade Policy: **

Exam regrade requests will be considered if:

## Homework

HW1 | Due Date: 2/5 | Problems: 2.12, 2.13, 2.14, 2.15 2.22 |
---|---|---|

HW2 | Due Date: 2/12 | Problems: 2.24, 2.26, 2.36, 2.37, 2.38 |

HW3 | Due Date: 2/21 | Problems: 3.3, 3.5, 3.11, 3.13, 3.16 |

HW4 | Due Date: 2/26 | Problems: 3.24, 3.25, 3.26, 3.27, 3.31 (For 3.31, you may find this file helpful) |

HW5 | Due Date: 3/5 | Problems: 5.5, 5.9, 5.13 and these two exercises |

HW6 | Due Date: 3/12 | Problems: 5.10, 5.11, 5.15 and this additional exercise |

HW7 | Due Date: 3/19 | See HW7.pdf |

HW8 | Due Date: 3/26 | Problems: 6.1, 6.2, 6.8, 6.9, 6.14 |

HW9 | Due Date: 4/16 | Problems: 4.2, 4.3, 4.7, 4.8, 4.9 |

HW10 | Due Date: 4/23 | Problems: 4.19 (Part 1 only), 4.21, 4.23, 4.25, 4.26 |

HW11 | Due Date: 5/7 | Problems: 9.1, 9.4, 10.2, 10.21, 11.4 |

** HW Notes: **

Questions for the HWs are from the Blum, Hopcroft and Kannan textbook (see above). Students are encouraged to work together but each must submit their own HW (written in their own words). Students must understand everything they turn in, and must show all their work to receive substantial credit. This includes all the relevant parts of their code for the coding questions and the assumptions made / parameters used that were not specified in the question text. Homeworks are due during class on the due date listed inside the chart above.

We recommend typesetting solutions in LaTeX or writing them neatly in dark pen; HW will be graded on BOTH Correctness and Neatness. If we cannot understand your solutions, we cannot give you points! Late HWs are **NOT** accepted unless the student has reasonable cause e.g. a doctor's appointment during class.

** HW Regrade Policy: **

Regrade requests will be considered if:

## Course Staff

Professor | John Hopcroft | Office hours by appointment only |
---|---|---|

TA | Eric Hans Lee | OH Wednesday 12:00pm-1:00pm, Gates G17 or by appointment |

TA | William Chen | OH Friday 8:00pm-9:00pm, Gates G19 |

TA | Jane Du | OH Thursday 6:00pm-7:00pm, Gates G15 |

TA | Tennyson Bardwell | OH Sunday 4:00pm-5:00pm, Gates G15 |

TA | Joshua Hull | OH Saturday 12:00pm-2:00pm, Gates G19 |

**Please email erichanslee@cs.cornell* for any administrative questions/inquiries.** Students struggling in the class or lacking certain background knowledge may opt for private tutoring sessions provided by either Joshua Hull or Jane Du; please email

`jth242@cornell.edu`

or `zd53@cornell.edu`

, respectively, to arrange a time and location. These tutoring sessions have been highly recommended by past students and have often greatly improved a student's academic performance.
**This course follows the Cornell University Code of Academic Integrity. Each student in this course is expected to abide by the Cornell University Code of Academic Integrity. Any work submitted by a student in this course for academic credit will be the student's own work. Violations of the rules (e.g. cheating, copying) will not be tolerated.