Behind numerous standard models and constructions in Data Science there is mathematics that makes things work. It is important to understand it to be successful in Data Science. In this specialisation we will cover wide range of mathematical tools and see how they arise in Data Science. We will cover such crucial fields as Discrete Mathematics, Calculus, Linear Algebra and Probability. To make your experience more practical we accompany mathematics with examples and problems arising in Data Science and show how to solve them in Python.
Discrete Math and Analyzing Social Graphs
The main goal of this course is to introduce topics in Discrete Mathematics relevant to Data Analysis.We will start with a brief introduction to combinatorics, the branch of mathematics that studies how to count. Basics of this topic are critical for anyone working in Data Analysis or Computer Science. We will illustrate new knowledge, for example, by counting the number of features in data or by estimating the time required for a Python program to run.
Next, we will apply our knowledge in combinatorics to study basic Probability Theory. Probability is everywhere in Data Analysis and we will study it in much more details later. Our goals for probability section in this course will be to give initial flavor of this field.
Finally, we will study the combinatorial structure that is the most relevant for Data Analysis, namely graphs. Graphs can be found everywhere around us and we will provide you with numerous examples. We will mainly concentrate in this course on the graphs of social networks. We will provide you with relevant notions from the graph theory, illustrate them on the graphs of social networks and will study their basic properties. In the end of the course we will have a project related to social network graphs.
As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in Python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in Data Analysis, starting from motivated high school students.
Calculus and Optimization for Machine Learning
Hi! Our course aims to provide necessary background in Calculus sufficient for up-following Data Science courses. Course starts with basic introduction to concepts concerning functional mappings. Later students are assumed to study limits (in case of sequences, single- and multivariate functions), differentiability (once again starting from single variable up to multiple cases), integration, thus sequentially building up a base for the basic optimisation. To provide an understanding of the practical skills set being taught, the course introduces the final programming project considering the usage of optimisation routine in machine learning.
Additional materials provided during the course include interactive plots in GeoGebra environment used during lectures, bonus reading materials with more general methods and more complicated basis for discussed themes.
First Steps in Linear Algebra for Machine Learning
The main goal of the course is to explain the main concepts of linear algebra that are used in data analysis and machine learning. Another goal is to improve the student’s practical skills of using linear algebra methods in machine learning and data analysis. You will learn the fundamentals of working with data in vector and matrix form, acquire skills for solving systems of linear algebraic equations and finding the basic matrix decompositions and general understanding of their applicability.This course is suitable for you if you are not an absolute beginner in Matrix Analysis or Linear Algebra (for example, have studied it a long time ago, but now want to take the first steps in the direction of those aspects of Linear Algebra that are used in Machine Learning). Certainly, if you are highly motivated in study of Linear Algebra for Data Sciences this course could be suitable for you as well.
Probability Theory, Statistics and Exploratory Data Analysis
Exploration of Data Science requires certain background in probability and statistics. This course introduces you to the necessary sections of probability theory and statistics, guiding you from the very basics all way up to the level required for jump starting your ascent in Data Science. The core concept of the course is random variable — i.e. variable whose values are determined by random experiment. Random variables are used as a model for data generation processes we want to study. Properties of the data are deeply linked to the corresponding properties of random variables, such as expected value, variance and correlations. Dependencies between random variables are crucial factor that allows us to predict unknown quantities based on known values, which forms the basis of supervised machine learning. We begin with the notion of independent events and conditional probability, then introduce two main classes of random variables: discrete and continuous and study their properties. Finally, we learn different types of data and their connection with random variables.
While introducing you to the theory, we'll pay special attention to practical aspects for working with probabilities, sampling, data analysis, and data visualization in Python.
This course requires basic knowledge in Discrete mathematics (combinatorics) and calculus (derivatives, integrals).
Each course of the specialisation ends with a project that gives an opportunity to see how the material of the course is used in Data Science. Each project is directed at solving practical problem in Data Science. In particular, in your projects you will analyse social graphs, predict estate prices and uncover hidden relations in the data.
As prerequisites we assume precollege level math, basic programming in python (functions, loops, recursion) and common sense. Our intended audience are all people that work or plan to work in Data Science.