Matematik 1

The course is read during the first semester in the Mathematical program, but can also be read as a freestanding course.

The course can be part of the following programmes: 1) Bachelor's Programme in Mathematics (N1MAT), 2) NMDSM and 3) Bachelor of Science Programme in Chemistry (N1KEM)

The aim of the course is to give a good basis for continued studies in mathematics. The course is divided into four modules: Introductory algebra, Linear Algebra I, Single variable calculus I, and Single variable calculus II. Furthermore, there is a component on written communication and a lab component.

Initial algebra: Logic and sets. Induction. Integer arithmetic. Functions and relations. Combinatorics. A little about groups, rings and fields. The structure of the number systems - mainly N, Z and Q.

Linear Algebra: Vector algebra. Linear equation systems and Gauss elimination. Linear (in)dependence. Linear transformations and their matrices. Vector spaces and subspaces in R^n. Eigenvalues and eigenvectors. Something about diagonalisation and
orthogonality. Matrix computations in Python.

Single variable calculus 1: Elementary functions. Limits. Continuity. Derivatives. Applications of derivatives on relevant problems, and associated calculations in Python.

Single variable calculus 2: Integrals. Taylor expansions. Differential equations. Applications of integrals on relevant problems, and associated calculations in Python.

Written communication: The basics of LaTex. Training to write a summary of information from several sources, lectures on the Professional Mathematics Day.

On successful completion of the course, the student will be able to:

• explain and use basic mathematical concepts, such as function and relation, limit and continuity, integrals and the fundamental theorem of calculus,
• explain and use basic methods in algebra, analysis and linear algebra,
• formulate important definitions and theorems in the course and prove some of them,
• carry out simple mathematical arguments and proofs, including proof by induction, on their own,
• differentiate a function and use the derivative for optimisation,
• analyse the behaviour of a function of one variable,
• solve simple ordinary differential equations,
• solve simple combinatorial problems,
• solve linear equation systems by means of Gauss elimination and analyse solvability,
• treat problems in linear geometry by means of vectors,
• show familiarity with linear transformations and analyse them by means of eigenvectors,
• use central information from several sources to write a summary which is correct both with regard to content and language, 
• give and receive feedback on writing in a constructive way.

There will be a written examination at the end of each module. During the course, there may be optional assignments that give bonus points on the exam. Examples of such components are tests, written assignments, laboratory sessions or project work. Information for the current course instance is given via the course homepage.

The course also includes compulsory written assignments and computer exercises. There is also compulsory attendance during the Professional Mathematics Day, including the
question time.

If a student, who has failed the same examined component twice, wishes to change examiner before the next examination, a written application shall be sent to the department responsible for the course and shall be granted unless there are special reasons to the contrary (Chapter 6, Section 22 of Higher Education Ordinance).

The grading scale comprises: Pass with Distinction (VG), Pass (G) and Fail (U). To obtain the grade Pass on the whole course, Pass is required on all four modules, as well as compulsory computer exercises and compulsory written assignments in written communication. If one furthermore has the grade Pass with distinction on at least 15 credits of the modules, one obtains the grade Pass with distinction on the whole course.

The course is evaluated with an anonymous questionnaire and/or a discussion with the student representatives. The results of and possible changes to the course will be shared with students who participated in the evaluation and students who are starting the
course.

For a list of course literature, see: https://studentportal.gu.se/dina-studier/kursplan-och-litteraturlista?f_nn=1&i_ma=1