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Regular version of the site
Bachelor 2018/2019

Mathematical Computations

Area of studies: Mathematics
When: 2 year, 4 module
Mode of studies: Full time
Language: English
ECTS credits: 3

Course Syllabus

Abstract

In this course, we learn how to use Mathematica and similar computer algebra systems (such as SageMath) in various mathematical problems. Mathematica is great for visualizing mathematical objects (such as functions, sets, polytopes etc.), for collecting empirical data and for testing conjectures. In particular, we focus on 3D graphics tools provided by Mathematica. These tools are ideal for drawing high precision pictures for mathematical papers. This is compulsory course. Pre-requisites: First year courses in Algebra, Analysis, Geometry, Discrete Mathematics and Topology
Learning Objectives

Learning Objectives

  • To study main principles of computer algebra systems
  • To apply Mathematica tools for solving problems from Algebra, Analysis, Combinatorics, Geometry, Number Theory and Topology
Expected Learning Outcomes

Expected Learning Outcomes

  • Can collect empirical data and test conjectures
  • Can draw high precision pictures for mathematical papers
  • Can visualize mathematical objects
Course Contents

Course Contents

  • Integer, rational, real and complex numbers and their presentation in Mathematica
  • Geometry in plane and 3-space and Mathematica tools for 2D and 3D graphics
  • Tables and lists in Mathematica; commands for working with lists; applications to matrices and polynomials
  • Mathematica tools for Analysis and Differential Equations; real and complex valued functions; continued fractions; animations for solutions of differential equations
  • Tools for Number Theory; breaking the RSA code
  • Combinatorics; tools for drawing graphs and computing their invariants
  • Tools for working with groups and permutations
Assessment Elements

Assessment Elements

  • non-blocking Midterm Test
  • non-blocking Project
Interim Assessment

Interim Assessment

  • Interim assessment (4 module)
    0.7 * Midterm Test + 0.3 * Project
Bibliography

Bibliography

Recommended Core Bibliography

  • Anastassiou, G. A., & Iatan, I. F. (2013). Intelligent Routines : Solving Mathematical Analysis with Matlab, Mathcad, Mathematica and Maple. Berlin: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=537150