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

COURSE DETAIL

MATHEMATICAL METHODS OF PHYSICS
Country
Sweden
Host Institution
Lund University
Program(s)
Lund University
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Physics Mathematics
UCEAP Course Number
154
UCEAP Course Suffix
UCEAP Official Title
MATHEMATICAL METHODS OF PHYSICS
UCEAP Transcript Title
MATH MTHDS PHYSICS
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description

The objective of the course is to teach the student more advanced mathematical tools an d methods that are useful in physics, and to apply these methods on concrete physical systems. Topics include analytic functions, special functions, Fourier analysis: Laplace transforms, ordinary differential equations, partial differential equations, and Green's functions. 

Language(s) of Instruction
English
Host Institution Course Number
FYTN01
Host Institution Course Title
MATHEMATICAL METHODS OF PHYSICS
Host Institution Course Details
Host Institution Campus
Science
Host Institution Faculty
Host Institution Degree
Host Institution Department
Physics
Course Last Reviewed
2021-2022
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MATHEMATICAL ANALYSIS I
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
114
UCEAP Course Suffix
A
UCEAP Official Title
MATHEMATICAL ANALYSIS I
UCEAP Transcript Title
MATH ANALYSIS I
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description

The course covers the concepts and methods of mathematical language. The focus is more on the analytic and topological notions such as convergence and continuity, which are essential for a rigorous treatment of mathematical analysis. The ability to read and write mathematical proofs is also further developed in this module. Topics include real numbers, sequences and series of real numbers, metrics in Euclidean spaces, open and closed sets, continuous functions, compact sets, connected sets, sequences of functions. Major applications include intermediate value theorem, extreme value theorem.

Language(s) of Instruction
English
Host Institution Course Number
MA2108
Host Institution Course Title
MATHEMATICAL ANALYSIS 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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COURSE DETAIL

RANDOM PROCESSES
Country
United Kingdom - England
Host Institution
University of London, Queen Mary
Program(s)
University of London, Queen Mary
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Statistics Mathematics
UCEAP Course Number
128
UCEAP Course Suffix
UCEAP Official Title
RANDOM PROCESSES
UCEAP Transcript Title
RANDOM PROCESSES
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This advanced course in probability introduces various probability models used in physical sciences, life sciences, and economics. It serves as an introduction to stochastic modeling and stochastic processes. The course covers discrete time processes including Markov chains, random walks, continuous time processes (such as Poisson processes), birth-death processes, and queuing systems.
Language(s) of Instruction
English
Host Institution Course Number
MTH 6141
Host Institution Course Title
RANDOM PROCESSES
Host Institution Course Details
Host Institution Campus
Queen Mary University of London
Host Institution Faculty
Host Institution Degree
Host Institution Department
Math
Course Last Reviewed
2019-2020
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PROBABILITY
Country
Hong Kong
Host Institution
Hong Kong University of Science and Technology (HKUST)
Program(s)
Hong Kong University of Science and Technology
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
121
UCEAP Course Suffix
UCEAP Official Title
PROBABILITY
UCEAP Transcript Title
PROBABILITY
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
Undergraduate level course in probability.Topics include Sample spaces, conditional probability, random variables, independence, discrete and continuous distributions, expectation, correlation, moment generating function, distributions of function of random variables, law of large numbers and limit theorems. Text: Sheldon Ross, A FIRST COURSE IN PROBABILITY.
Language(s) of Instruction
English
Host Institution Course Number
MATH2421
Host Institution Course Title
PROBABILITY
Host Institution Course Details
Host Institution Campus
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
Course Last Reviewed
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INDUSTRIAL APPLICATIONS:MODELLING AIRCRAFT ICING (LEVEL 2)
Country
United Kingdom - England
Host Institution
University College London
Program(s)
Summer at University College London
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Physics Mathematics Engineering
UCEAP Course Number
130
UCEAP Course Suffix
S
UCEAP Official Title
INDUSTRIAL APPLICATIONS:MODELLING AIRCRAFT ICING (LEVEL 2)
UCEAP Transcript Title
AIRCRAFT ICING
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description

This course is in the interdisciplinary field of icing in relation to aircraft. Ultimately, this course will draw from mathematics, physics, chemistry and engineering to provide attendees with a broad overview of the field of aircraft icing, and how the problem may be approached mathematically. This  involves understanding the problem, discussing the current state of engineering solutions, and study of how mathematics can help to improve, enhance and further this field. Modelling of this phenomena is a threefold approach. Firstly, the trajectory of particles within the fluid flow concerning an oncoming aircraft is calculated. Secondly, the behavior and mechanics of impinging particles (particles that make contact with the aircraft) needs to be understood. Thirdly, how ice builds up on a surface alongside the possibility of it shedding are important.
This course serves as an introduction to understanding this field and the analytical modelling of this problem.

Language(s) of Instruction
English
Host Institution Course Number
ISSU0082
Host Institution Course Title
INDUSTRIAL APPLICATIONS:MODELLING AIRCRAFT ICING (LEVEL 2)
Host Institution Course Details
Host Institution Campus
Bloomsbury
Host Institution Faculty
Host Institution Degree
Bachelors
Host Institution Department
Department of Mathematics
Course Last Reviewed
2022-2023
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MATHEMATICAL AND STATISTICAL METHODS A
Country
Ireland
Host Institution
Trinity College Dublin
Program(s)
Trinity College Dublin
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics Economics
UCEAP Course Number
108
UCEAP Course Suffix
UCEAP Official Title
MATHEMATICAL AND STATISTICAL METHODS A
UCEAP Transcript Title
MATH & STAT METHODS
UCEAP Quarter Units
4.00
UCEAP Semester Units
2.70
Course Description
This course develops students knowledge of calculus, with increased depth of coverage and further applications. The course consolidates and develops skills previously learned so as to provide a basis for further calculus studies.
Language(s) of Instruction
English
Host Institution Course Number
EC2140
Host Institution Course Title
MATHEMATICAL AND STATISTICAL METHODS A
Host Institution Course Details
Host Institution Campus
Trinity College Dublin
Host Institution Faculty
Host Institution Degree
Host Institution Department
Economics
Course Last Reviewed
2018-2019
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DISCRETE MATHEMATICS
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
102
UCEAP Course Suffix
E
UCEAP Official Title
DISCRETE MATHEMATICS
UCEAP Transcript Title
DISCRETE MATH
UCEAP Quarter Units
5.00
UCEAP Semester Units
3.30
Course Description
This course offers an introduction to discrete mathematics and its applications to computer science. Topics include set theory, binary relations, lattices, elementary counting techniques, recurrence, linear recurrence equations, the generating function and its relevance in combinatorics and recurrence problems, graph theory, modeling, algorithms, ordering and enumerations problems, equivalence relations. Previous coursework in calculus and algebra is required.
Language(s) of Instruction
English
Host Institution Course Number
15971
Host Institution Course Title
MATEMÁTICA DISCRETA
Host Institution Course Details
Host Institution Campus
Escuela Politécnica Superior. (Leganés)
Host Institution Faculty
Host Institution Degree
Host Institution Department
Ciencia e Ingeniería de Materiales e Ingenieria Química
Course Last Reviewed
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FINANCIAL MATHEMATICS
Country
Ireland
Host Institution
University College Dublin
Program(s)
University College Dublin
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
102
UCEAP Course Suffix
UCEAP Official Title
FINANCIAL MATHEMATICS
UCEAP Transcript Title
FINANCIAL MATH
UCEAP Quarter Units
4.00
UCEAP Semester Units
2.70
Course Description
This course introduces financial and commodity derivatives markets and their most commonly traded securities. Securities such as forwards, futures, and options have been traded on exchanges, as well as "over the counter," for decades. The emphasis of this course is on the pricing of such derivative securities. The course starts by looking at future and forward contracts to understand their properties and differences and determine how to value them. After a detailed study of the different types of options, the valuation method of binomial trees (based on the Cox, Ross, and Rubenstein paper of 1979) is discussed. The course then studies the model of a share price evolution introduced by Black, Scholes, and Merton in 1973, and derives the Black-Scholes model for valuing European call and put options on a non-dividend-paying stock. A brief introduction to probability theory is also provided in the course.
Language(s) of Instruction
English
Host Institution Course Number
MST30030
Host Institution Course Title
FINANCIAL MATHEMATICS
Host Institution Course Details
Host Institution Campus
UC Dublin
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematical Studies
Course Last Reviewed
2018-2019
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ADVANCED MATHEMATICS
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
106
UCEAP Course Suffix
UCEAP Official Title
ADVANCED MATHEMATICS
UCEAP Transcript Title
ADV MATHEMATICS
UCEAP Quarter Units
5.00
UCEAP Semester Units
3.30
Course Description

This course covers ordinary differential equations and partial differential equations. Topics include: first-order differential equations; second-order linear equations; systems of first-order linear equations; nonlinear systems and stability; separation of variables; boundary-value problems.

Pre-requisites: Calculus I, Calculus II, and Linear Algebra.

Language(s) of Instruction
English
Host Institution Course Number
15331
Host Institution Course Title
AMPLIACIÓN DE MATEMÁTICAS
Host Institution Course Details
Host Institution Campus
Leganés
Host Institution Faculty
Escuela Politécnica Superior
Host Institution Degree
Grado en Ingeniería Aeroespacial
Host Institution Department
Matemáticas
Course Last Reviewed
2022-2023
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COURSE DETAIL

PROBABILITY
Country
Spain
Host Institution
Complutense University of Madrid
Program(s)
Complutense University of Madrid
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
121
UCEAP Course Suffix
UCEAP Official Title
PROBABILITY
UCEAP Transcript Title
PROBABILITY
UCEAP Quarter Units
5.00
UCEAP Semester Units
3.30
Course Description
This course studies the principle elements of probability theory. Topics covered include: introduction to probability theory, randomized experiments; probability spaces, conditional probability and independence of events; dimensional random variables (distribution function, discrete and continuous variables, transformations, moments, characteristic function and moment generating function, notable distributions); multidimensional random variables (marginal and conditional distributions, independence, transformations, moments, characteristic function, correlation coefficient, notable distributions); Stochastic convergence (convergence of random variables, relationships and properties, laws of large numbers, central limit theorems). An understanding of analysis and algebra is recommended. Texts: V Quesada & A García Pérez. Lecciones de Cálculo de Probabilidades. Díaz de Santos, 1988. VK Rohatgi. An Introduction to Probability Theory and Mathematical Statistics. Wiley, 1976. R Vélez & V Hernández. Cálculo de Probabilidades 1. UNED, 1995. R Vélez. Cálculo de Probabilidades 2. Ediciones Académicas, 2004.
Language(s) of Instruction
Spanish
Host Institution Course Number
800583
Host Institution Course Title
PROBABILIDAD
Host Institution Course Details
Host Institution Campus
Facultad de Ciencias Matemáticas, Campus Ciudad Universitaria
Host Institution Faculty
Host Institution Degree
Host Institution Department
Departamento de Estadística e Investigación Operativa
Course Last Reviewed
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