Mathematics for Data Science 1

Welcome to the semester 1, 2019 version of MATH7501. This is a bridging course in the Masters of Data Science program at the University of Queensland. The course is designed to bring students up to speed with mathematical concepts from discrete mathematics, calculus and elementary linear algebra - all with a view of data science, statistics and machine learning applications that follow. The course is recommended for data science students that have not taken more than 2 dedicated mathematics courses in their undergraduate degree.

The prerequisite for the course is to have basic knowledge of high-school mathematics, including algebra, geometry, (basic) trigonometry, working with functions, logarithms and related concepts of a similar level.

The goal of the course is to enable the students to speak the "language of mathematics" in a way sufficient for understanding further data science, statistics and machine learning concepts. Since the course material is quite broad, there is less emphasis on the detailed mechanics, and more detail on the concepts at hand. As such, the course closely follows the course reader. This document accompanies the students throughout the semester.

Some motivating uses of the mathematics covered will be presented from 20 methods of the data scientist and the mathematics behind them. This is an evolving manuscript, also to be used in the the second semester course MATH7502.

The course assessment includes 5 homework assignments, 3 quizzes and a final exam. Some of the homework assignments are to be solved "by hand" while others need to be carried out computationally using Wolfram Mathematica. Most Mathematica based problems are taken from this collection of Mathematica based exercises created by Sam Hambleton.

Home assignments are to be submitted individually with each student submitting a unique assignment (copying assignments will not be tolerated). Nevertheless, students are encouraged to collaborate and discuss the homework assignments in an open and constructive manner. Sharing ideas, helping each other and jointly working towards a goal is great.

Students may also look at resources from last year's course.

The prerequisite for the course is to have basic knowledge of high-school mathematics, including algebra, geometry, (basic) trigonometry, working with functions, logarithms and related concepts of a similar level.

The goal of the course is to enable the students to speak the "language of mathematics" in a way sufficient for understanding further data science, statistics and machine learning concepts. Since the course material is quite broad, there is less emphasis on the detailed mechanics, and more detail on the concepts at hand. As such, the course closely follows the course reader. This document accompanies the students throughout the semester.

Some motivating uses of the mathematics covered will be presented from 20 methods of the data scientist and the mathematics behind them. This is an evolving manuscript, also to be used in the the second semester course MATH7502.

The course assessment includes 5 homework assignments, 3 quizzes and a final exam. Some of the homework assignments are to be solved "by hand" while others need to be carried out computationally using Wolfram Mathematica. Most Mathematica based problems are taken from this collection of Mathematica based exercises created by Sam Hambleton.

Home assignments are to be submitted individually with each student submitting a unique assignment (copying assignments will not be tolerated). Nevertheless, students are encouraged to collaborate and discuss the homework assignments in an open and constructive manner. Sharing ideas, helping each other and jointly working towards a goal is great.

Students may also look at resources from last year's course.

The course is coordinated by Yoni Nazarathy (y.nazarathy@uq.edu.au) and the tutor is Vincent Mellor (vam103@maths.uq.edu.au). The study format is as follows:

- Lectures take place on Wednesdays during 8:00AM - 9:50AM. There are 13 lectures in total. Prior to each lecture, students are expected to follow the on-line material and the study material provided below. The focus of the lectures is to tie the mathematics concepts from the material to more specific data-science methods and applications. The focus of the lectures is not to introduce the material. Nevertheless, a review of the material studied by the students before the lecture will be presented. Yoni Nazarathy will be available after the lecture to answer specific questions.

- Look out for blackboard messages indicating which material needs to be covered prior to the lectures.

- Of the 13 lectures, 3 are allocated for quizzes. The duration of each quiz is 70 minutes, starting at 8:05AM. The reminader of the quiz lecture will be to quickly review the quiz answers (after students finish the quiz). The quiz dates appear in the course profile.

- Tutorials take place on Fridays during 1:00PM - 1:50PM. The purpose of the tutorial is for the students to work on their homework assignments with the tutor guding the students as they tackle questions. Tutorials may also include review exercises, preparing the students for quizzes and the final exam.

- Students are encouraged to communicate, both with each other, and with the course staff (as needed) via the course's slack workspace: Please join the slack workspace. Messages from the course staff will also be disseminated via blackboard and sometimes slack.

- Homework assignments are to be handed in at the start of the tutorial on the dates provided in the course profile. Late assignments will not be accepted.

Below are links to supporting material for the course, some of which needs to be covered prior to the lectures:

- Unit 1 - Sets, number systems, counting and cardinality

- Unit 2 - Relations and functions

- Unit 3 - Foundations in logic

- Unit 4 - Sequences, their limits and series

- Unit 5 - Real functions: Limits and continuity

- Unit 6 - Elementary Matrix Operations

- Unit 7 - Derivatives, Optimisation and basic ODEs

- Unit 8 - Linear approximations and Taylor series

- Unit 9 - Integration

- Unit 10 - Vectors and partial derivatives

Below are homework assignments, quizzes and solutions:

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