Discipline ID
97ac1514-598d-4ae9-af20-fdf75b940953
COURSE DETAIL
NUMERICAL METHODS
Country
Spain
Host Institution
Carlos III University of Madrid
Program(s)
Carlos III University of Madrid
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
114
UCEAP Course Suffix
C
UCEAP Official Title
NUMERICAL METHODS
UCEAP Transcript Title
NUMERICAL METHODS
UCEAP Quarter Units
5.00
UCEAP Semester Units
3.30
Course Description
This course discusses different concepts of numerical analysis including algorithms, stability, accuracy, and efficiency. Topics include: errors, algorithms, and estimates; nonlinear equations and nonlinear systems; methods for linear systems of equations; polynomial interpolation-- Lagrange, Hermite, piecewise, and splines; numerical quadrature and differentiation.
Prerequisites: Linear Algebra, Differential Calculus, Integral Calculus, and Programming.
Language(s) of Instruction
English
Host Institution Course Number
18262
Host Institution Course Title
CÁLCULO NUMÉRICO
Host Institution Course Details
Host Institution Campus
Leganés
Host Institution Faculty
Escuela Politécnica Superior
Host Institution Degree
Grado en Matemática Aplicada y Computación
Host Institution Department
Departamento de Matemáticas
Course Last Reviewed
2022-2023
COURSE DETAIL
METRIC SPACES
Country
Ireland
Host Institution
University of Galway
Program(s)
University of Galway
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
103
UCEAP Course Suffix
UCEAP Official Title
METRIC SPACES
UCEAP Transcript Title
METRIC SPACES
UCEAP Quarter Units
4.00
UCEAP Semester Units
2.70
Course Description
This course is an introduction the theory of metric spaces. The real line with its natural notion of distance is a metric space, from which the metric space definition and theory evolves. Familiar concepts such as convergence and continuity are explored in this new broader context while new concepts and properties, such as closed sets and compactness, illuminate key facts about functions.
Language(s) of Instruction
English
Host Institution Course Number
MA341
Host Institution Course Title
METRIC SPACES
Host Institution Course Details
Host Institution Campus
National University of Ireland, Galway
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed
2019-2020
COURSE DETAIL
QUANTITATIVE METHODS AND MATHEMATICAL THINKING
Country
United Kingdom - England
Host Institution
University College London
Program(s)
University College London
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Statistics
Mathematics
UCEAP Course Number
114
UCEAP Course Suffix
UCEAP Official Title
QUANTITATIVE METHODS AND MATHEMATICAL THINKING
UCEAP Transcript Title
QUANTITATVE METHODS
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
In this course, students learn how to understand, analyze, and resolve complex problems using a range of quantitative techniques. Emphasis is placed on the importance of understanding the science and techniqies behind these ideas in engaging with the modern world. Students tackle estimation problems, learn coding with Python, and explore statistics and game theory.
Language(s) of Instruction
English
Host Institution Course Number
BASC0003
Host Institution Course Title
QUANTITATIVE METHODS AND MATHEMATICAL THINKING
Host Institution Course Details
Host Institution Campus
University College London
Host Institution Faculty
Host Institution Degree
Host Institution Department
Arts and Sciences (BASc)
Course Last Reviewed
2023-2024
COURSE DETAIL
INTRODUCTION TO NUMBER THEORY
Country
United Kingdom - England
Host Institution
King's College London
Program(s)
King's College London
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
141
UCEAP Course Suffix
UCEAP Official Title
INTRODUCTION TO NUMBER THEORY
UCEAP Transcript Title
INTRO NUMBER THEORY
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This course provides an introduction to elementary number theory and to further develop the algebraic techniques met in "Introduction to Abstract Algebra" (is this italicized or in quotes... seems like the name of a book?). This course prepares students for more demanding modules in number theory and algebra by introducing several new concepts in the concrete setting of rational integers. This course includes a review of divisibility, prime numbers and congruences; residue class rings, Euler's f-function, and primitive roots; quadratic residues and quadratic reciprocity law; irrational and transcendental numbers, sums of squares; and some Diophantine equations.
Language(s) of Instruction
English
Host Institution Course Number
5CCM224A
Host Institution Course Title
INTRODUCTION TO NUMBER THEORY
Host Institution Course Details
Host Institution Campus
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed
2024-2025
COURSE DETAIL
INTRODUCTION TO PROBABILITY
Country
United Kingdom - England
Host Institution
University of London, Queen Mary
Program(s)
University of London, Queen Mary
UCEAP Course Level
Lower Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
65
UCEAP Course Suffix
UCEAP Official Title
INTRODUCTION TO PROBABILITY
UCEAP Transcript Title
INTRO PROBABILITY
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This course is an introduction to probability, covering events and random variables. It introduces the basic concepts of probability theory and develops them to the stage where one can begin to use probabilistic ideas in statistical inference, modeling, and the study of stochastic processes.Topics include the axioms of probability, conditional probability, independence, random variables, expectation, and variance. Joint distributions are covered briefly.
Language(s) of Instruction
English
Host Institution Course Number
MTH4107/MTH4207
Host Institution Course Title
INTRODUCTION TO PROBABILITY
Host Institution Course Details
Host Institution Campus
Queen Mary University of London
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematical Sciences
Course Last Reviewed
COURSE DETAIL
PROBABILITY AND STATISTICS 2
Country
United Kingdom - England
Host Institution
King's College London
Program(s)
King's College London
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Statistics
Mathematics
UCEAP Course Number
108
UCEAP Course Suffix
UCEAP Official Title
PROBABILITY AND STATISTICS 2
UCEAP Transcript Title
PROB & STATISTICS 2
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
Topics cover include: Bivariate probability, continuous densities, generating functions. The exponential densities, including normal, t-, χ2 and F. Simple parametric and nonparametric tests. Further topics include the consistency, efficiency and sufficiency of estimates, maximum likelihood estimation; the central limit theorem, Chebyshev's inequality, the Neyman-Pearson lemma and the likelihood ratio test; regression, and analysis of variance.
Language(s) of Instruction
English
Host Institution Course Number
5CCM241A
Host Institution Course Title
PROBABILITY & STATISTICS II
Host Institution Course Details
Host Institution Campus
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed
2022-2023
COURSE DETAIL
DIFFERENTIAL FORMS
Country
Ireland
Host Institution
University of Galway
Program(s)
University of Galway
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
104
UCEAP Course Suffix
UCEAP Official Title
DIFFERENTIAL FORMS
UCEAP Transcript Title
DIFFERENTIAL FORMS
UCEAP Quarter Units
4.00
UCEAP Semester Units
2.70
Course Description
The course explains Stokes' formula. The formula is best explained using the differential forms language of Élie Cartan. The course covers the case p=0 (8 lectures), the case p=1 (8 lectures), the case p= 2 (8 lectures), and explains how Stokes' formula can be applied to the usual problems of multivariate calculus, financial mathematics, and electromagnetism.
Language(s) of Instruction
English
Host Institution Course Number
MA2286
Host Institution Course Title
DIFFERENTIAL FORMS
Host Institution Course Details
Host Institution Campus
NUI Galway
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed
2018-2019
COURSE DETAIL
REAL ANALYSIS
Country
Norway
Host Institution
University of Oslo
Program(s)
University of Oslo
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
111
UCEAP Course Suffix
UCEAP Official Title
REAL ANALYSIS
UCEAP Transcript Title
REAL ANALYSIS
UCEAP Quarter Units
8.00
UCEAP Semester Units
5.30
Course Description
This course is a continuation of Calculus and Linear Algebra. The theory is generalized from finite dimensional spaces to spaces that may be infinite dimensional, and whose elements typically are functions, rather than numbers or what was previously considered as vectors. The course discusses key concepts including convergence, continuity, differentiability, completeness, and compactness. The theory is applied to problems from differential equations and Fourier analysis. The course provides training in mathematical reasoning and lays the theoretical foundation for further studies in mathematical analysis. The course requires students to have met specific prerequisites in order to enroll in the course.
Language(s) of Instruction
English
Host Institution Course Number
MAT2400
Host Institution Course Title
REAL ANALYSIS
Host Institution Course Details
Host Institution Campus
Mathematics and Natural Sciences
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed
COURSE DETAIL
HONORS DIFFERENTIAL EQUATIONS
Country
United Kingdom - Scotland
Host Institution
University of Edinburgh
Program(s)
University of Edinburgh
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
137
UCEAP Course Suffix
UCEAP Official Title
HONORS DIFFERENTIAL EQUATIONS
UCEAP Transcript Title
DIFFERENTL EQUATNS
UCEAP Quarter Units
8.00
UCEAP Semester Units
5.30
Course Description
This is a course on differential equations discussing higher order linear equations, Laplace transforms, systems of First Order Linear ODEs, non-linear systems of ODEs, Fourier Series, use of separation of variables in standard PDEs, and Sturm-Liouville Theory. In the skills section of the course, students work on symbolic manipulation, computer algebra, graphics, and a final project. Python is used in computer labs.
Language(s) of Instruction
English
Host Institution Course Number
MATH10066
Host Institution Course Title
HONOURS DIFFERENTIAL EQUATIONS
Host Institution Course Details
Host Institution Campus
Edinburgh
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed
COURSE DETAIL
ANALYSIS IN QUANTUM INFORMATION THEORY
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
153
UCEAP Course Suffix
UCEAP Official Title
ANALYSIS IN QUANTUM INFORMATION THEORY
UCEAP Transcript Title
QUANTUM INFO THEORY
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This course provides the analytic background behind quantum information theory in the framework of operators on Hilbert spaces and functional analysis. Topics include completely positive and completely bounded maps; operator systems and spaces; Choi representation and Kraus operators; Stinespring's representation theorem; tensor products; quantum measurements and related sets of correlations; entanglement; Schmidt decompositions; and factorizable channels and applications in quantum information theory.
Language(s) of Instruction
English
Host Institution Course Number
NMAK22000U
Host Institution Course Title
ANALYSIS IN QUANTUM INFORMATION THEORY
Host Institution Course Details
Host Institution Campus
Host Institution Faculty
Faculty of Science
Host Institution Degree
Master
Host Institution Department
Department of Mathematical Sciences
Course Last Reviewed
2022-2023