Discipline ID
97ac1514-598d-4ae9-af20-fdf75b940953

COURSE DETAIL

DISCRETE MATHEMATICS
Country
Netherlands
Host Institution
Maastricht University – University College Maastricht
Program(s)
University College Maastricht
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
103
UCEAP Course Suffix
UCEAP Official Title
DISCRETE MATHEMATICS
UCEAP Transcript Title
DISCRETE MATH
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
In this course students learn the what the following fundamental concepts involve: numbers, a.o. integers, natural numbers, real numbers and prime numbers and properties that these classes of numbers have; logic, drawing conclusions and how to use logic to prove mathematical statements; sets, properties of sets and concepts related to sets, like intersections, and unions; mathematical relations, a comparing mechanism for elements in a set, several relations and their properties; functions, mapping from one set to another, properties of functions, like invertibility; combinatorics, the science of smart counting, permutations and combinations. Almost every time mathematics is used, it concerns some of the above concepts. Students who are interested in (applied) mathematics, computer science and/or econometrics might find this course particularly useful.
Language(s) of Instruction
English
Host Institution Course Number
SCI2002
Host Institution Course Title
DISCRETE MATHEMATICS
Host Institution Course Details
Host Institution Campus
University College Maastricht
Host Institution Faculty
Host Institution Degree
Host Institution Department
Science
Course Last Reviewed

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ALGEBRA III
Country
United Kingdom - England
Host Institution
Imperial College London
Program(s)
English Universities,Imperial College London
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
142
UCEAP Course Suffix
UCEAP Official Title
ALGEBRA III
UCEAP Transcript Title
ALGEBRA III
UCEAP Quarter Units
5.00
UCEAP Semester Units
3.30
Course Description
In this course, students study the following topics: rings, integral domains, unique factorization domains, modules, ideals homomorphisms, quotient rings, submodules quotient modules, fields, maximal ideals, prime ideals, principal ideal domains, Euclidean domains, rings of polynomials, Gauss's lemma, Eisenstein's criterion, field extensions, Noetherian rings and Hilbert's basis theorem, dual vector space, tensor algebra and Hom, basics of homological algebra, and complexes and exact sequences.
Language(s) of Instruction
English
Host Institution Course Number
M3P8
Host Institution Course Title
ALGEBRA III
Host Institution Course Details
Host Institution Campus
Imperial College London
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed

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PROBABILITY AND STATISTICS
Country
Taiwan
Host Institution
National Taiwan University
Program(s)
National Taiwan University
UCEAP Course Level
Lower Division
UCEAP Subject Area(s)
Statistics Mathematics
UCEAP Course Number
27
UCEAP Course Suffix
UCEAP Official Title
PROBABILITY AND STATISTICS
UCEAP Transcript Title
PROBABILITY & STATS
UCEAP Quarter Units
4.50
UCEAP Semester Units
3.00
Course Description

This course covers the theory, models, and analysis of probability and basic statistics and their applications with emphasis on electrical and computer engineering problems. The main topics are: Experiments, Model, and Probabilities, Random Variables, Random Variables and Expected Value, Random Vectors, Sums of Random Variables, Parameter Estimation Using the Sample Mean, and Hypothesis Testing. Text: R.D. Yates and D.J. Goodman, PROBABILITY AND STOCHASTIC PROCESSES. Assessment: midterm exam (35%), final exam (35%), homework and problems (25%), participation (5%).

Language(s) of Instruction
Host Institution Course Number
EE2007
Host Institution Course Title
PROBABILITY AND STATISTICS
Host Institution Campus
Host Institution Faculty
Host Institution Degree
Host Institution Department
Electrical Engineering
Course Last Reviewed
2022-2023

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COMBINATORICS AND GRAPHS
Country
Singapore
Host Institution
National University of Singapore
Program(s)
National University of Singapore
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
110
UCEAP Course Suffix
A
UCEAP Official Title
COMBINATORICS AND GRAPHS
UCEAP Transcript Title
COMBINATORICS
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description

This course introduces fundamental principles and techniques in combinatorics as well as the basics of graph theory, which have practical applications in such areas as computer science and operations research. The major topics from combinatorics are: Permutations and Combinations, Binomial and Multinomial Coefficients, Principle of Inclusion and Exclusion, Generating Functions, Recurrence Relations. The major topics from graph theory are: Basic Concepts and Results, Bipartite graphs and trees.

 

Language(s) of Instruction
English
Host Institution Course Number
MA2214
Host Institution Course Title
COMBINATORICS AND GRAPHS I
Host Institution Course Details
Host Institution Campus
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed
2022-2023

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LINEAR ALGEBRA II WITH LAB
Country
Korea, South
Host Institution
Korea University
Program(s)
Korea University
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
127
UCEAP Course Suffix
B
UCEAP Official Title
LINEAR ALGEBRA II WITH LAB
UCEAP Transcript Title
LINEAR ALGEBRA/LAB
UCEAP Quarter Units
4.50
UCEAP Semester Units
3.00
Course Description

The course covers introductory linear algebra, focusing on the eigenvalues and eigenvectors of a matrix, orthogonality, and properties of positive definite matrices. The eigenvalues and eigenvectors are considered from their definitions to their applications. Other topics include orthogonal projections, the Gram-Schmidt process, and the inner product space. 

Language(s) of Instruction
English
Host Institution Course Number
MATH222
Host Institution Course Title
LINEAR ALGEBRA II WITH LAB
Host Institution Course Details
Host Institution Campus
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed
2022-2023

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ANALYSIS 4: REAL ANALYSIS
Country
United Kingdom - England
Host Institution
University College London
Program(s)
University College London
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
124
UCEAP Course Suffix
UCEAP Official Title
ANALYSIS 4: REAL ANALYSIS
UCEAP Transcript Title
REAL ANALYSIS
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This course reinforces and extends analysis of a single variable to topics including uniform convergence. The concept of a metric space is then developed to produce results generalizing those in one variable. Topics include pointwise and uniform convergence, the Weierstrass approximation theorem, orthonormal systems and Fourier Series, normed and metric spaces, Banach contraction mapping theorem, continuity, compactness, and spectral norms.
Language(s) of Instruction
English
Host Institution Course Number
MATH0051
Host Institution Course Title
ANALYSIS 4: REAL ANALYSIS
Host Institution Campus
University College London
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed
2019-2020

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ADVANCED PROBABILITY THEORY 1
Country
Denmark
Host Institution
University of Copenhagen
Program(s)
University of Copenhagen
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
155
UCEAP Course Suffix
UCEAP Official Title
ADVANCED PROBABILITY THEORY 1
UCEAP Transcript Title
ADV PROB THEORY 1
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This course covers the following: sequences of random variables, almost sure convergence, Kolmogorov's 0-1 law; the strong law of large numbers; weak convergence of probability measures; characteristic functions; the central limit theorem; triangular arrays and Lindebergs condition; the multivariate central limit theorem; the ergodic theorem.
Language(s) of Instruction
English
Host Institution Course Number
NMAK11003U
Host Institution Course Title
ADVANCED PROBABILITY THEORY 1
Host Institution Course Details
Host Institution Campus
Science
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematical Sciences
Course Last Reviewed

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INTERNATIONAL INTERNSHIP
Country
Czech Republic
Host Institution
CEA CAPA, Prague
Program(s)
Summer Internship, Prague
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Urban Studies Statistics Psychology Political Science Mathematics Legal Studies International Studies Health Sciences Film & Media Studies Environmental Studies Engineering Education Economics Computer Science Communication Business Administration Art Studio Architecture
UCEAP Course Number
187
UCEAP Course Suffix
UCEAP Official Title
INTERNATIONAL INTERNSHIP
UCEAP Transcript Title
INTRNTNL INTERNSHIP
UCEAP Quarter Units
9.00
UCEAP Semester Units
6.00
Course Description

The International Internship course develops vital business skills employers are actively seeking in job candidates. This course is comprised of two parts: an internship, and a hybrid academic seminar. Students are placed in an internship within a sector related to their professional ambitions. The hybrid academic seminar, conducted both online and in-person, analyzes and evaluates the workplace culture and the daily working environment students experience. The course is divided into eight career readiness competency modules as set out by the National Association of Colleges and Employers (NACE), which guide the course’s learning objectives. During the academic seminar, students reflect weekly on their internship experience within the context of their host culture by comparing and contrasting their experiences with their global internship placement with that of their home culture. Students reflect on their experiences in their internship, the role they have played in the evolution of their experience in their internship placement, and the experiences of their peers in their internship placements. Students develop a greater awareness of their strengths relative to the career readiness competencies, the subtleties and complexities of integrating into a cross-cultural work environment, and how to build and maintain a career search portfolio.

Language(s) of Instruction
Host Institution Course Number
INT430
Host Institution Course Title
INTERNATIONAL INTERNSHIP
Host Institution Course Details
Host Institution Campus
CEA CAPA
Host Institution Faculty
Host Institution Degree
Host Institution Department
Course Last Reviewed
2022-2023

COURSE DETAIL

ALGEBRA AND LOGIC
Country
Australia
Host Institution
University of Sydney
Program(s)
University of Sydney
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
123
UCEAP Course Suffix
UCEAP Official Title
ALGEBRA AND LOGIC
UCEAP Transcript Title
ALGEBRA AND LOGIC
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This course unifies and extends mathematical ideas and techniques that most participants will have met in their first and second years, and will be of general interest to all students of pure and applied mathematics. It combines algebra and logic to present and answer a number of related questions of fundamental importance in the development of mathematics, from ancient to modern times. The Propositional and Predicate Calculi are studied as model axiomatic systems in their own right, including proofs of consistency and completeness. The final part of the course introduces precise notions of computability and decidability, through abstract Turing machines, culminating in the unsolvability of the Halting Problem the undecidability of First Order Logic, and a discussion of Godel's Incompleteness Theorem. Classical and novel arithmetics are introduced, unified and described abstractly using field and ring axioms and the language of field extensions. Quotient rings are introduced, which are used to construct different finite and infinite fields. A construction of the real numbers, by factoring out rings of Cauchy sequences of rationals by the ideal of null sequences, is presented. Axiomatics are placed in the context of reasoning within first order logic and set theory.
Language(s) of Instruction
English
Host Institution Course Number
MATH3066
Host Institution Course Title
ALGEBRA AND LOGIC
Host Institution Course Details
Host Institution Campus
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed

COURSE DETAIL

LINEAR ANALYSIS
Country
Sweden
Host Institution
Lund University
Program(s)
Lund University
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
143
UCEAP Course Suffix
UCEAP Official Title
LINEAR ANALYSIS
UCEAP Transcript Title
LINEAR ANALYSIS
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This course covers the following: numerical series and convergence criteria; function series, power and Fourier series, absolute and uniform convergence, pointwise convergence; important theorems about Fourier series: Parseval's formula, Bessel's inequality, convergence theorems; cosine and sine series; applications within classical partial differential equations; the Fourier transform, theory and applications.
Language(s) of Instruction
English
Host Institution Course Number
MATB24
Host Institution Course Title
LINEAR ANALYSIS
Host Institution Course Details
Host Institution Campus
Science
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed
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