# Major Applied Mathematics

### Mathematical background of Major Applied Mathematics

There are formal requirements to enroll in the program. They guarantee for instance that students have at least a background in mathematics comparable to `mathematics B' (wiskunde B) at vwo high school level. This concerns mainly skills (like problem solving skills, mathematical thinking, algebraic skills), functions (like exponential, logarithmic and trigonometric functions), graphs, equations, differentiation and integration, geometry with coordinates. The vwo elective Wiskunde D is *not a prerequisite* for the bachelor program, but provides a valuable addition to students' background.

### Major Applied Mathematics

The Bachelor program Applied Mathematics aims at educating students in the main branches of mathematics relevant for applications in a societal and industrial setting, including working on real-world mathematical modeling problems. This makes up about half of the program, the mathematics major.

The remaining part of the program consists of various `common' courses aimed at all TU/e students, a wide range of elective courses to choose from to deepen or widen one's knowledge inside or outside mathematics, and courses focusing on the role of the engineer in society. The training of relevant professional skills is also part of the program.

The bachelor final project at the end of the third year provides students with their first substantial mathematical research experience.

The bachelor program primarily prepares for the subsequent master program Industrial and Applied Mathematics.

The detailed objectives of the program are as follows.

### 1. Mathematical knowledge and understanding

- To know the mathematics that is part of the fundamental knowledge of an academically trained mathematician as defined by international standards, characterized by abstraction, a clear method of reasoning and mastery of the basic techniques.
- To understand and know those parts and aspects of mathematics that are important for the application of mathematics to practical problems.

### 2. Mathematical operational skills

- To have knowledge and skills with respect to basic mathematical and computer science techniques, in particular in relation to the design of algorithms for mathematical solution approaches, and to be able to implement and process these algorithms using generally available standard software.
- To be acquainted with application areas of mathematics.

### 3. Research- and design skills

- To be able to find relevant sources and literature and appreciate their importance.
- To be able to carry out a supervised mathematical research assignment of limited scope, possibly in the form of a literature study.
- To have the ability to design and handle simple mathematical models in a team using mathematical solution approaches and to have the skills to validate these solution approaches.

### 4. Academic and professional skills

- To have a critical and creative attitude when working on problems and studying mathematical theories and methods.
- To be able to plan one’s work on mathematical problems, application or design oriented problems, and the study of mathematical theories, either in a team or alone, and to reflect on one’s own work.
- To be able to convey (mathematical) results both orally and in writing to specialists, and, in general terms, to non-specialists.
- To have insight in the role and responsibility of the mathematician in society.

### Thematic lines Applied Mathematics

Content wise, we distinguish the following thematic lines

in the major Applied Mathematics:

**Basic courses on Analysis**

Courses: Analysis 1, Analysis 2, Analysis 3**Basic courses on Algebra and Linear Algebra**

Courses: Set theory and algebra, Linear algebra 1, Linear algebra 2**Further courses on Computational Science and Engineering (CSE)**

Courses: Introduction numerical analysis, Ordinary differential equations, Complex analysis, Functional analysis**Further courses on Discrete Mathematics and its Applications (DMA)**

Courses: Algebra and discrete mathematics, Algorithmic algebra and number theory, Graph theory and combinatorics**Further courses on Statistics, Probability, and Operations Research (SPOR)**

Courses: Probability Theory, Mathematical Statistics, Stochastic processes, Linear statistical models, Linear optimization**Mathematical Modelling**

Concerns parts of the courses: Programming and Modelling (2 ects, 1^{st}year), Introduction numerical analysis (1 ects, 2^{nd}year), Probability theory (1 ects, 2^{nd}year), Ordinary differential equations (1 ects, 2^{nd}year), Stochastic processes (1 ects, 2^{nd}year) and the course Mathematical modelling (5 ects, 3^{rd}year).**Professional Skills**

This concerns the skills lines Cooperating, Presenting, Writing, Reflecting,

Planning and Organizing, Searching and processing (scientiﬁc) information.

These skills lines are part of various major courses and account for 5 ects in total.**Programming skills and Mathematical Software**

Programming skills and handling mathematical software are part of various major courses. It concerns LaTeX (mathematical document preparation system), Mathematica, Matlab, Statistical software (R), Programming in Python.**Research Experience**

This concerns the Bachelor Final Project

**Note:**

The thematic lines 1, 2, 3, 4, 5 consist of regular courses. In these courses a part Modelling and/or Professional Skills and/or Mathematical Software can be contained. The themes 3, 4, 5 prepare for the main specializations CSE, DMA and SPOR in the master program Industrial and Applied Mathematics.