Applied Mathematics Minor

The course begins with a review of functions and their graphs, after which students are introduced to the concepts of differentiation and integration. Understanding is reinforced through extensive practical work, with a strong emphasis on applications in economics, statistics and management science.

This computer-based course presents the main concepts in Statistics: the concept of random variables, frequency, and probability distributions, variance and standard deviation, kurtosis and skewness, probability rules, Bayes theorem, and posterior probabilities. Important statistical methods like Contingency analysis, ANOVA, Correlation analysis and Regression Analysis are introduced and their algorithms are fully explained. The most important probability distributions are introduced: Binomial, Poisson, and Normal distribution, as well as the Chebyshev theorem for non-known distributions. Inferential statistics, sampling distributions, and confidence intervals are covered to introduce statistical model building and single linear regression. Active learning and algorithmic learning are stressed. Emphasis is put both on algorithms –methods and assumptions for their applications. Excel is used while calculators with STAT buttons are not allowed. Ultimately students are required to make a month-long research project, select the theoretical concept they want to test, perform a literature review, find real data from Internet databases or make their surveys, apply methods they studied in the class, and compare theoretical results with their findings. Research is done and presented in groups, papers are Individual. Selected SPSS or Excel Data Analysis examples are also provided.

The first half of the course gives an introduction into Linear Algebra. Vectors and vector spaces, analytical geometry, matrices and linear equations, and their rank, and also determinants are discussed. The second half of the course discusses the theory of partial and total derivatives for functions of several variables. Topics considered here are limits, partial derivatives, chain rule, gradients, and optimization with or without restrictions.

This course is an elementary introduction to Game Theory. It focuses on how to ana-lyze situations and make rational decisions based on the information gathered. Students will analyze parlor games, gambling, and real-world situations. As mathematical basis for the analysis, Probability Theory and some Algebra are needed, but will be developed in detail

Discrete Mathematics approaches questions that are finite in nature. Combinatorics provides formulas for the numbers of certain mathematical ''objects''. An example is to find the number of different ways one can fill a given rectangle with dominos. With the rise of the computer in the second half of the last century, optimization problems became more prominent, where one is supposed to find a ''best'' substructure in a given discrete structure. An example is to find a shortest path from A to B in a finite network. Counting principles, from simple ones to recurrence relations and generating functions, are presented, and algorithms for optimization problems on different discrete structures, like graphs, partially ordered sets, and others, are introduced and analyzed. The roles of proofs and algorithms for these questions are discussed thoroughly. Public key cryptography is also covered.

Undergraduate research project in mathematics. The goal is to produce a research paper on a topic selected together with the instructor, and to submit it to some journal for undergraduate research in mathematics. Presentation at some conference on undergraduate research is also encouraged.

In the first part of this course students learn concepts in inferential statistics, its main principles and algorithms. They learn how to apply sampling distributions in the case of business random variables, how to state and test business hypotheses about population mean or proportion differences, how to calculate ANOVA table components, and how to deploy estimation methods to provide information needed to solve real business problems. In the second part of the course, students learn advanced model building methods, algorithms needed to make and test dynamic multiple regression models and time series (ARMA) models. In addition to teaching and learning methods based on the textbook, problem-based learning (PBL) and interactive engagement (IE) are used. Many internet data bases, EXCEL add-ins and EViews are used to enhance IE based learning. Selected SPSS or STATA examples are also provided.

This course offers an introduction to computer programming using some high level language. Students will learn how to formulate, represent, and solve problems using the computer. Emphasis will be on the features common to most of these languages. After introducing data structures, expressions, functions, control structures, input and output, the course will proceed to classes, events, user interface construction, documentation, and program testing. Both procedural and object-oriented programming paradigms will be discussed.

The course investigates in a simple but rigorous way some of the fundamental issues of modern microeconomics, exploring the main concepts of game theory, as well as the basic elements of the economics of information, and of contract theory. A solid background on these topics is essential to the investigation of strategic decision making, the assessment of the relevance of asymmetric and/or incomplete information in decision processes, and the design of contracts. These, in turn, are among the most important issues that firms and individuals commonly need to face in all situations in which the consequences of individual decisions are likely to depend on the strategic interactions among agents' actions, and on the signaling value of information. Proceeding from intuition to formal analysis, the course investigates the methodological approach of game theory (allowing for a systematic analysis of strategic interaction) and the main concepts of the economics of information (allowing to assess the effects of asymmetric or incomplete information on agents' decisions). Further, it combines both game theory and economics of information to provide an introduction to the essential elements of contract theory.