Entry requirements

General entry requirements and Mathematics 4/Mathematics D

Learning outcomes

On completion of the course, the student should be able to:

• give an account of important concepts and definitions in the area of the course;
• exemplify and interpret important concepts in specific cases;
• formulate important results and theorems covered by the course;
• describe the main features of the proofs of important theorems;
• express problems from relevant areas of applications in a mathematical form suitable for further analysis;
• use the theory, methods and techniques of the course to solve mathematical problems;
• present mathematical arguments to others.

Content

Elementary logic: truth tables and disjunctive and conjunctive normal forms. Set theory: intersection, union, complement, Cartesian product, and power set. Relationships between open statements and subsets. The concept of functions: properties such as injective, surjective, bijective, and inverse functions, with illustrative examples using exponential functions, trigonometric functions, and polynomial functions. Relations: equivalence relations and equivalence classes. Combinatorics: the multiplication principle, permutations and combinations, the binomial theorem. Natural and whole numbers: induction, recursion, divisibility, prime numbers, Euclid's algorithm, congruence calculations, representation of numbers in different bases. Linear congruences, the Chinese remainder theorem. Complex numbers: the complex plane, argument, absolute value, and polar form. Rational, real, and complex polynomials: factorization, irreducible polynomials, Euclid's algorithm, multiple roots, rational roots of polynomials with integer coefficients.

Instruction

Lectures, lessons. 

Assessment

Written examination at the end of the course. Optional written test that gives bonus points at the first summative assessment. The optional test is only given once. 

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other regulations

Cannot be included in the same degree as any of the courses 1MA010 Basic Course in Mathematics and 1MA004 Algebra I.