Foundations of Mathematics

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: Bachelor's Programme in Mathematics (N1MAT).

Basic propositional and predicate logic. Basic set theory. Cardinality. Induction and recursion. Functions, operators and relations, including equivalence relations. Modular arithmetic. Integers and divisibility. Prime numbers and the fundamental theorem of arithmetic. Linear Diophantine equations. Basic combinatorics. Binomial theorem. Permutations. The structure of the number system: N, Z, Q and R.

After passing the course, the student should be able to:

• formulate and use important definitions and theorems in the course and be able to prove some of the theorems,
• perform simple mathematical reasoning and proofs, including by induction and contradiction, 
• solve basic combinatorial problems,
• solve linear Diophantine equations and equations in Z_n, 
• determine the validity of logical arguments.

The course is assessed by means of a written exam at the end of the course. During the course, there may be optional assignments that give bonus points on the exam. Examples of such assignemnts are tests, written assignments, laboratory sessions or project work. Information for the current course instance is given via the course homepage.

If a student who has been failed twice for the same examination element wishes to change examiner before the next examination session, such a request is to be granted unless there are specific reasons to the contrary (Chapter 6 Section 22 HF).

If a student has received a certificate of disability study support from the University of Gothenburg with a recommendation of adapted examination and/or adapted forms of assessment, an examiner may decide, if this is consistent with the course’s intended learning outcomes and provided that no unreasonable resources would be needed, to grant the student adapted examination and/or adapted forms of assessment.

If a course has been discontinued or undergone major changes, the student must be offered at least two examination sessions in addition to ordinary examination sessions. These sessions are to be spread over a period of at least one year but no more than two years after the course has been discontinued/changed. The same applies to placement and internship (VFU) except that this is restricted to only one further examination session.

If a student has been notified that they fulfil the requirements for being a student at Riksidrottsuniversitetet (RIU student), to combine elite sports activities with studies, the examiner is entitled to decide on adaptation of examinations if this is done in accordance with the Local rules regarding RIU students at the University of Gothenburg.

The grading scale comprises: Pass with Distinction (VG), Pass (G) and Fail (U).

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.

An earlier version of this course was previously included as a sub-course in MMG200 Mathematics 1. It is not permitted to be examined on both this course and the sub-course Introductory Algebra in MMG200 Mathematics 1.

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