Program Overview
Program Overview
The University of Copenhagen offers a Bachelor's program in Machine Learning and Data Science, which includes a course in Mathematical Analysis (MatAn).
Course Description
The course provides an introduction to mathematical analysis, focusing on its later application in data science and machine learning. The course is methodically mathematically stringent, including proofs, to give a deep insight into fundamental concepts. The course content includes concepts such as convergence, differentiability, and integrability, which are used to analyze functions in one and several variables.
Course Content
The following topics will be covered in the course:
- Talfølger and talrækker
- Functions of one variable: continuity, differentiability, and Riemann integral
- Function sequences and function series: pointwise and uniform convergence, power series, and Fourier series
- Functions of several variables: continuity, differentiability, and Taylor approximation
- Functions of several variables: extremum investigation, convexity, compactness, and optimization
Learning Objectives
By the end of the course, the student will:
- know convergence criteria for talfølger and talrækker
- know basic concepts, such as continuity, differentiability, and integrability, related to functions of one or several variables
- know convergence concepts and criteria for function sequences and function series, including power series and Fourier series
Skills
By the end of the course, the student will be able to:
- handle the mathematical analysis boundary value concept with technical safety
- perform mathematical analysis of functions in one variable, i.e., investigate continuity, differentiability, integrability, and extremum investigation of functions
- perform mathematical analysis of functions from several variables to several variables, specifically extremum investigation and optimization
Competencies
By the end of the course, the student will be able to:
- determine the correctness and relevance of mathematical arguments within analysis
- argue with mathematical stringency in definitions and proof
- analyze problem statements from the multidimensional mathematical analysis, including evaluating the relevance of differential and integral calculus in concrete contexts
Recommended Prerequisites
Introduction to mathematics (MatIntro), Linear Algebra (LinAlg or LinAlgDat)
Teaching Methods
4 hours of lectures and 4 hours of exercises per week for 7 weeks
Workload
- Category
- Hours
- Lectures
- 28
- Preparation (estimated)
- 146
- Theoretical exercises
- 28
- Exam
- 4
- Total
- 206
Assessment
The exam is a 4-hour written exam with supervision. The student must pass 5 assignments, each of which must be passed.
Evaluation Criteria
The student must demonstrate that they meet the course's learning objectives.
Course Information
- Language: Danish
- Course code: NMAB20001U
- Points: 7.5 ECTS
- Level: Bachelor
- Duration: 1 block
- Placement: Block 1
- Schedule group: A (Tuesday 8-12 + Thursday 8-17)
- Course capacity: No limit – unless you sign up in the late registration period (BA and KA) or as a merit or single-course student
Study Board
- Study Board for Mathematics and Computer Science
Offering Institute
- Department of Mathematical Sciences
Offering Faculty
- Faculty of Science
Course Responsible
- Matthias Christandl
Timetable
- 25E-B1-1; Hold 01; ; Mathematical Analysis
- 25E-B1-1; Hold 02; ; Mathematical Analysis
- 25E-B1-1; Hold 03; ; Mathematical Analysis