Unit 1: Basic matrix calculus

Unit 2:  Vector spaces and linear mappings

Unit 3: Equation systems and linear mappings, inner products

Unit 4: Orthogonality and diagonalization, basic topology

Unit 5: Basic Topology and  Calculus; convexity and separation;

Unit 6: Multivariable differentation

Unit 7: Optimization,

Unit 8:  final exam

The course is devoted to Advanced Mathematics for Business and Finance. All notions from Basic Mathematics and Undergraduate Mathematics are supposed to be well-known and familiar. After completing this course the student will have the ability to:

• describe and explain the basic concepts and definitions of applied linear algebra (in particular vector spaces and linear mappings; inner products, orthogonality and diagonalization; orthogonal projections; convexity and separation), of multivariable differentiation, and of optimization
• work with the basic concepts and definitions of applied linear algebra, of multivariable differentiation  and of optimization. Moreover, this course contributes to the student's ability to:
• confidently organize and integrate mathematical ideas and information.
• shift mathematical material quickly and efficiently, and to structure it into a coherent mathematical argument.
• solve applied problems where skills are required from linear algebra, multivariable differentiation and integration, and from optimization

Full attendance is compulsory. This means that students should attend at least 80% of all lectures, at most one lecture can be missed.

• This course is taught as a lecture accompanied with homework assignments.

• The lectures are aimed at providing and explaining the basic concepts and definitions and illustrate them with examples. the (mandatory) homework assignments will help students to comprehend the key ideas and to train problem-solving skills. The homework assignments will be discussed  in a enrichment course by Gabriela Kovacova   that accompanies the lecture.
• At present (as of September 6) , the plan is  to hold the lecture in the standard classroom format. Students are expected to be on campus,  there will be no parallel online classes. Please note that exams (entrance exam, midterm and final) will be held on campus.   I intend to have on-site examinations even if a worsening of the Corona situation should require  a switch to online classes.

Assessment:

• 20% Written exam after unit 1/bridging course
• 10% Results from assignments
• 25% Results from midterm exam (on october 20)
• 45% Final exam

Instead of the written test after unit 1 the result of the "QF Bridging Course Mathematics" (by Andrea Wagner) can be used. Note however, that the entrance exam takes precedence over the bridging course result, so if you take part in the entrance exam the result from the entrance exam  result counts.  There will not be any training for the entrance  exam in the first unit. For the skills, knowledge and readings necessary to pass the entrance exam see "Prerequisites and/or admission requirements" ("Notwendige Vorkenntnisse/Aufnahmeverfahren").
For passing the course a minimum score of 50% of total points is needed; moreover, students need to reach at least 45% of the points in the final.

The following notions are subject of every basic course in business mathematics. In particular, they are part of the introductory mathematics course at WU.

• Basic Business Mathematics (introductory algebra, introductory equations, functions of one variable, differentiation, single-variable optimization, integration, interest rates, functions of several variables, multivariable optimization, constrained optimization, matrix and vector algebra)

The following notions are standard content of undergraduate business mathematics. In particular, they can be obtained from elective courses of undergraduate studies at WU.

• Undergraduate Business Mathematics (introductory mathematical foundations, properties of functions, advanced differentiation, advanced integration, trigonometric functions and complex numbers, sets-completeness-convergence)

Reading: K. Sydsaeter and P. Hammond (2008), Essential Mathematics for Economic Analysis. Prentice Hall, Third Edition. ISBN 978-0-273-71324-1.