Mathematics with computers

2022/2023
Programme:
Mathematics, Second Cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
core mandatory
Group:
R1
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
1
Seminar
2
Tutorial
2
Lab
0
Content (Syllabus outline)

Students learn how to use software for solving mathematical problems. The course focuses on the practical aspects and proficient use of software. The following areas of computerized mathematics are covered (suggested software is listed in parentheses):
analysis (Mathematica, Sage)
discrete mathematics (Mathematica, Sage, Vega, Pajek)
algebra (Mathematica, Sage, Magma, GAP)
topology and geometry (Mathematica, Sage, GeoGebra, various specialized programs for topology invariants)
statistics and financial mathematics (R)
logic (Isabelle, Coq, HOL, Agda)

Readings

Uporabniški priročniki za programsko opremo.
User manuals and other documentation for the software at hand.

Objectives and competences

Introduction to and application of specialized software for doing mathematics.
With individual presentations and team work interactions within seminar/project activities students acquire communication and social competences for successful team work and knowledge transfer.

Intended learning outcomes

Knowledge and understanding:
Practical knowledge and use of advanced programs for solving mathematical problems.
Application:
Application of computers in mathematics.
Reflection:
Modern computer technology has become an indispensable tool in mathematics.
Transferable skills:
The emphasis on practical use and applications enables the student to use computers in all other courses.

Learning and teaching methods

Lectures, exercises, project course, homeworks, consultations

Assessment

Course project
Project presentation and defense
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Andrej Bauer:
BAUER, Andrej, STONE, Christopher A. RZ: a tool for bringing constructive and computable mathematics closer to programming practice. Journal of logic and computation, ISSN 0955-792X, 2009, vol. 19, no. 1, str. 17-43. [COBISS-SI-ID 15325785]
BAUER, Andrej, CLARKE, Edmund, ZHAO, Xudong. Analytica - An experiment in combining theorem proving and symbolic computation. Journal of automated reasoning, ISSN 0168-7433, 1998, vol. 21, no. 3, str. 295-325. [COBISS-SI-ID 10606425]
BAUER, Andrej, PETKOVŠEK, Marko. Multibasic and mixed hypergeometric Gosper-type algorithms. Journal of symbolic computation, ISSN 0747-7171, 1999, let. 28, št. 4-5, str. 711-736. [COBISS-SI-ID 9210969]