Unit 1: Vector Spaces and linear mappings

Unit 2: Linear mappings and equation systems

Unit 3: Inner products, orthogonality and diagonalization

Unit 4: Convexity and separation; Basic Calculus

Unit 5: Multivariable differentation and optimization

Unit 6: Optimization, Ordinary Differential Equations

Unit 7:  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 differential equations.
• work with the basic concepts and definitions of applied linear algebra, of multivariable differentiation  and of differential equations.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 differential equations.

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  that accompanies the lecture.

Assessment:

• 25% written exam after unit 1
• 5% Results from assignments
• 25% Result from midterm exam
• 45% endterm examination

Instead of the written test after unit 1 the result of the "QF Bridging Course Mathematics" (by Andrea Wagner) can be used. The decision whether to write the exam or to use the result of the Bridging Course has to be announced by thursday, 4.10. There will not be any training for the exam in the first unit. For the skills, knowledge and readings necessary to pass the first exam see "Prerequisites and/or admission requirements" ("Notwendige Vorkenntnisse/Aufnahmeverfahren"). Further information on the assessment will be provided.

To pass the course students  have to reach at least 40% of the points in the final exam.

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.