Mathematics

This course offers a basic study of business and economics statistics. It discusses probability theory, distribution models, sampling, and descriptive statistics. By using realistic examples from the current economic environment, students practice solving problems.  

This course offers a study of the most relevant properties of finite dimensional inner product spaces, its related applications (with special emphasis on least squares problems), and the classes and factorizations of matrices related to them. It also discusses general bilinear forms in finite dimensional vector spaces. Specific topics include: orthogonality; unitary matrices; QR factorization; bilinear and quadratic forms; Schur triangularization theorem; Spectral Theorem; singular value decomposition (SVD). 

Pre-requisites: Linear Algebra; Calculus; Fundamentals of Mathematics 

This course covers the general theory of vector spaces as a continuation of Linear Algebra I. The course discusses general vector spaces (including complex vector spaces); linear independence; linear transformations and their matrix representations, and metric vector spaces.

Required course prerequisite: Linear Algebra I.
 

A course for undergraduate and graduate students majoring in math and statistics, covering Martingale, stationary processes and the Brownian motion.

Algebra II provides an introduction to commutative algebra, on which both algebraic geometry and algebraic number theory are built. In fact, commutative algebra provides the tools for local studies in algebraic geometry, much like multivariate calculus is the main tool for local studies in differential geometry. This course closely follows "Introduction to Commutative Algebra" by Atiyah and Macdonald but may be complemented with some additional material, e.g. concerning Gröbner bases.The prerequisite course Algebra I explained the basic notions of algebra: groups, rings, fields, and factor structures, culminating in Galois theory.

The course covers a selection from the following topics: homotopy sets, homotopy groups and the Hurewicz theorem, fibrations and cofibrations, generalized homology theories and spectra, bundles and classifying spaces, characteristic classes, low-dimensional topology, geometric group theory, spectral sequences and cohomology operations. The methods presented are illustrated by applications to various classical problems in algebraic topology.

This course provides a foundational introduction to the basics of actuarial science, focusing on the theory of interest and life contingencies and their application to lifecycle planning. It explores key actuarial models to analyze essential financial concepts, including economic balance sheets, personal net worth, human capital, assets, liabilities, and the fundamentals of retirement planning. In light of rapid advancements in artificial intelligence, this course emphasizes the practical integration of these technologies. Students will learn to harness the power of large language models (LLMs) to assist in and elevate the actuarial analysis of financial scenarios. 

This course examines complex numbers; vector spaces: row and column vectors (real and complex), linear combinations, abstract vector spaces, bases and dimension of vector spaces; linear maps: definitions and examples, matrix of a linear map, composition, invertibility and isomorphisms; solving systems of linear equations using linear algebra; determinants: definition and properties; eigenvectors and eigenvalues: definitions, diagonalisation of matrices, canonical forms of 2x2 matrices.

The course covers the foundational mathematical techniques (algebra, matrices, and calculus) required to understand finance, with an emphasis on applications (time value of money, portfolio optimization, and derivative securities).

This course focuses on utilizing a computer to master mathematical skills. Starting with the basic usage of Octave (or MATLAB), the class instructs on how one can solve various mathematical problems by writing and executing simple programs.