Discipline ID
97ac1514-598d-4ae9-af20-fdf75b940953
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
HONORS DIFFERENTIAL EQUATIONS
Host Institution Campus
Edinburgh
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
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 Campus
Host Institution Faculty
Faculty of Science
Host Institution Degree
Master
Host Institution Department
Department of Mathematical Sciences
COURSE DETAIL
COMBINATORICS AND PROBABILITY
Country
United Kingdom - Scotland
Host Institution
University of St Andrews
Program(s)
Scottish Universities,Psychology and Neuroscience, St Andrews,University of St Andrews
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
104
UCEAP Course Suffix
UCEAP Official Title
COMBINATORICS AND PROBABILITY
UCEAP Transcript Title
COMBINATORICS &PROB
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This course provides an exploration into the study of combinatorics and finite sets and also the study of probability. It describes the links between these two areas of study. It provides a foundation both for further study of combinatorics within pure mathematics and for the various statistics courses that are available.
Language(s) of Instruction
English
Host Institution Course Number
MT2504
Host Institution Course Title
COMBINATORICS AND PROBABILITY
Host Institution Campus
St Andrews
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics & Statistics
COURSE DETAIL
LINEAR MATHEMATICS 2
Country
United Kingdom - Scotland
Host Institution
University of St Andrews
Program(s)
Scottish Universities,Psychology and Neuroscience, St Andrews,University of St Andrews
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
109
UCEAP Course Suffix
UCEAP Official Title
LINEAR MATHEMATICS 2
UCEAP Transcript Title
LINEAR MATH 2
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This course continues the study of vector spaces and linear transformations begun in MT2501. It shows the importance of linearity in many areas of mathematics ranging from linear algebra through to geometric applications to linear operators and special functions. The main topics include diagonalization and the minimum polynomial, Jordan normal form, inner product spaces, orthonormal sets and the Gram-Schmidt process, and adjoint and self-adjoint operators.
Language(s) of Instruction
English
Host Institution Course Number
MT3501
Host Institution Course Title
LINEAR MATHEMATICS 2
Host Institution Campus
St Andrews
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics & Statistics
COURSE DETAIL
DIFFERENTIAL EQUATION
Country
China
Host Institution
Fudan University
Program(s)
Fudan University
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
173
UCEAP Course Suffix
UCEAP Official Title
DIFFERENTIAL EQUATION
UCEAP Transcript Title
DIFFERENTL EQUATION
UCEAP Quarter Units
4.50
UCEAP Semester Units
3.00
Course Description
Many phenomena in natural sciences and social sciences can be summarized as quantitative relationships expressed by differential equations. In particular, many laws in economics and finance can be described by differential equations. This course enables non-mathematics students to master the basic theories and methods of differential equations, and to cultivate their logical thinking ability and the ability to apply differential equations to solve practical problems. The course consists of two parts: ordinary differential equations and partial differential equations. The main topics include: first-order ordinary differential equations, high-order ordinary differential equations, linear ordinary differential equations, difference equations, basic partial differential equations (harmonic equation, heat conduction equation, wave equation), mathematical model of differential equations.
Language(s) of Instruction
Chinese
Host Institution Course Number
Econ130105
Host Institution Course Title
DIFFERENTIAL EQUATION
Host Institution Campus
Host Institution Faculty
Wu Hao
Host Institution Degree
Host Institution Department
Mathematical Science
COURSE DETAIL
GEOMETRY AND GROUPS
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
115
UCEAP Course Suffix
UCEAP Official Title
GEOMETRY AND GROUPS
UCEAP Transcript Title
GEOMETRY & GROUPS
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This course introduces basic examples in geometry, builds up fundamental understanding of curvature, and enhances familiarity with groups and group actions outside of pure algebra.
Language(s) of Instruction
English
Host Institution Course Number
MATH0052
Host Institution Course Title
GEOMETRY AND GROUPS
Host Institution Campus
University College London
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
COURSE DETAIL
PROBABILITY AND STATISTICS I
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
117
UCEAP Course Suffix
UCEAP Official Title
PROBABILITY AND STATISTICS I
UCEAP Transcript Title
PROBABILITY&STATS 1
UCEAP Quarter Units
6.00
UCEAP Semester Units
4.00
Course Description
This course introduces the basic concepts and computations of probability theory as well as the statistical analysis of data and the main statistical tests. It examines elementary combinatorial analysis, the definition of probability, unions and intersections, statistical independence, exclusivity and exhaustibility, conditional probability, Bayes' theorem, discrete and continuous random variables, binomial distribution, Poisson distribution, normal distribution, descriptive statistics, correlation and regression, hypothesis tests, and confidence intervals.
Language(s) of Instruction
English
Host Institution Course Number
4CCM141A
Host Institution Course Title
PROBABILITY AND STATISTICS I
Host Institution Campus
King's College London
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
COURSE DETAIL
INTRODUCTION TO NUMERICAL ANALYSIS
Country
United Kingdom - England
Host Institution
Imperial College London
Program(s)
Imperial College London
UCEAP Course Level
Upper Division
UCEAP Subject Area(s)
Mathematics
UCEAP Course Number
150
UCEAP Course Suffix
UCEAP Official Title
INTRODUCTION TO NUMERICAL ANALYSIS
UCEAP Transcript Title
NUMERICAL ANALYSIS
UCEAP Quarter Units
5.00
UCEAP Semester Units
3.30
Course Description
This applied analysis course leads to an introduction to some of the standard algorithms in numerical analysis. Students explore orthogonality, alongside inner/outer products on Rn; linear dependence/independence; orthogonal/orthonormal vectors; classical Gram-Schmidt; orthogonal matrices; Givens rotations, QR factorization, and Cauchy-Schwartz inequality. The course also covers gradients/Hessians, exploring Taylor series for f: Rn à? R; classification of stationary points; positive definite matrices; generalized inner products on Rn; and Cholesky factorization of symmetric positive definite matrices.
Language(s) of Instruction
English
Host Institution Course Number
M2AA3
Host Institution Course Title
INTRODUCTION TO NUMERICAL ANALYSIS
Host Institution Campus
Imperial College London
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematics
COURSE DETAIL
LINEAR ALGEBRA
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
105
UCEAP Course Suffix
UCEAP Official Title
LINEAR ALGEBRA
UCEAP Transcript Title
LINEAR ALGEBRA
UCEAP Quarter Units
5.00
UCEAP Semester Units
3.30
Course Description
This course covers the concepts of complex numbers, systems of linear equations, vector space in Cn, matrix algebra, eigenvalues and eigenvectors, orthogonality, and normal matrices.
Language(s) of Instruction
Host Institution Course Number
16266,14182,15363
Host Institution Course Title
LINEAR ALGEBRA
Host Institution Campus
Leganés
Host Institution Faculty
Escuela Politécnica Superior
Host Institution Degree
Grado en Ciencia e Ingeniería de Datos
Host Institution Department
Matemáticas
COURSE DETAIL
HISTORY OF 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
103
UCEAP Course Suffix
UCEAP Official Title
HISTORY OF MATHEMATICS
UCEAP Transcript Title
HISTORY OF MATH
UCEAP Quarter Units
4.00
UCEAP Semester Units
2.70
Course Description
This course gives a brief scientific account of various topics including number theory, graph theory, analysis, and combinatorics in the history of mathematics.
Language(s) of Instruction
English
Host Institution Course Number
MST30020
Host Institution Course Title
HISTORY OF MATHEMATICS
Host Institution Campus
UC Dublin
Host Institution Faculty
Host Institution Degree
Host Institution Department
Mathematical Studies