This course covers the essential mathematical concepts and techniques needed for data science, tailored for students with a background in high school mathematics but no prior university-level mathematics. The focus will be on building a solid understanding of linear algebra, calculus, and optimisation, which are foundational for data science.
1. Linear Algebra (1.1 Importance of mathematics in data science. , 1.2 Mathematical notation and language. , 1.3 Sets, functions, and relations. , 1.4 Introduction to vectors and their properties. , 1.5 Operations with vectors addition, scalar multiplication. , 1.6 Introduction to matrices and matrix operations. , 1.7 Matrix addition, multiplication, and transposition. , 1.8 Identity and inverse matrices. , 1.9 Solving linear equations using matrices. , 1.10 Determinants of matrices. , 1.11 Properties of determinants. , 1.12 Introduction to eigenvalues and eigenvectors. , 1.13 Linear transformations and their matrix representations. , 1.14 Applications of linear transformations in data science. , 1.15 Singular value decomposition SVD Theory)
2. Calculus (2.1 Basics of limits and continuity. , 2.2 Introduction to differentiation. , 2.3 Rules of differentiation. , 2.4 Derivatives in data science. , 2.5 Optimization using derivatives finding maxima and minima. , 2.6 Taylor series and approximations. , 2.7 Basics of integration. , 2.8 Fundamental Theorem of Calculus. , 2.9 Techniques of integration. , 2.10 Functions of several variables. , 2.11 Partial derivatives and their applications.)
3. Applications in Data Science (3.1 Optimisation basics. , 3.2 Constrained and unconstrained optimisation. , 3.3 Introduction to gradient descent.)
By the end of the course, students should be able to do the following:
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SCQF Level: 11
Credits: 15