The curriculum of the UGM Mathematics Master’s Degree Study Program curriculum is designed to produce Strata 2 (S2) graduates with an M.Sc. (Master of Science) which has the following competencies:
A. Main Competencies:
A1. In Knowledge and Understanding:
- Able to master theories and concepts about algebra, analysis, mathematical statistics, and their applications that are relevant to their area of expertise;
- Be open and responsive to the development of science, especially mathematics and its applications;
- Possess basic scientific insights and abilities and technical skills needed to adapt and or create new concepts;
- Familiar with the latest thinking of experts in the field of mathematics and its applications;
- Being able to apply mathematics according to their field of expertise to solve various problems including those that require cross-disciplinary approaches;
- Having the ability to develop scientific concepts in the field of mathematics through independent research.
A2. In terms of Intellectual (thinking) Skills:
Able to think logically, analytically, inductive, deductive, and structured.
B. Supporting Competencies:
B1. Practical Skill: Graduates who have the ability to do problem-solving, computing manually or with the help of computers.
B2. Transferable Skill: Graduates who are able to communicate effectively for mathematical material and its applications.
C. Other Competencies: have noble character
Taking into account the development of science and professions related to Mathematics, as well as input from all stakeholders, the curriculum of the Mathematics Study Program of the Faculty of Mathematics and Natural Sciences UGM was revised in 2007. In 2012 a minor revision of the curriculum was made with the main change being the development and addition of interest in the study program.
Starting the 2022/2023 Academic Year, the UGM Mathematics Study Program offer 4 (four) interests, namely
- Analysis,
- Algebra and combinatorics,
- Applied Mathematics and computation,
- Statistics, Data Sciences, and Actuarial Sciences.
The selection of interests is determined no later than at the beginning of the second semester.
The following is a description of each Area of Interest.
Area of Interest in Analysis
Analysis (from the ancient Greek word ἀνάλυσις, meaning a breaking-up, an untying; from the words: ana (throughout) and lysis (a loosening)) is the process of breaking down complex problems or substances into smaller parts to gain a better understanding.
Mathematical Analysis, often abbreviated as analysis, is a branch of mathematics that studies problems related to continuous change, the approximation of a mathematical object (such as numbers and functions) by other objects. For example, numbers are studied using sequences of numbers, and functions are studied using limits (infinitesimal methods). Analysis also examines problems related to the spaces formed by collections of objects equipped with concepts of nearness (proximity) and distance (metric). Analysis can be viewed as an evolution of calculus, encompassing the fundamental concepts and techniques of analysis. Analysis also evolves by generalizing and abstracting concepts and properties from the real number system, such as distance, length, and order. Analysis teaches and trains analytical and systematic thinking, which can help solve new, non-standard problems. Therefore, Mathematical Analysis is an important foundation for developing concepts and methods, both within mathematical analysis itself, other branches of mathematics outside analysis, and its applications.
Analysis includes, among other things, real analysis (such as the real number system, sequences, limits, derivatives, real functions) and its generalizations/abstractions (such as metric spaces), complex analysis, differential and integral equations, measure theory and integral, functional analysis (including operator theory, function spaces, sequence spaces, Riesz spaces), topology, and fixed-point theory.
Area of Interest in Algebra and Combinatorics
Algebra is one of the branches of mathematics that studies mathematical symbols and the rules for manipulating these symbols. The scope of algebra study ranges from simple tasks like solving equations to abstractions that give rise to groups, rings, and fields. The simpler aspects of algebra are often used in other fields, such as economics, engineering, or applied mathematics. Meanwhile, abstract algebra is a subject of research for mathematicians, with potential applications in other fields.
Besides being the name of a branch of mathematics, algebra is also the name of a mathematical system or structure. Over time, specific algebras have become research objects in the field of algebra, such as linear algebra, Lie algebra, non-associative algebra, commutative algebra, topological algebra, and so on. Furthermore, the algebraic approach is often applied to specific objects, such as algebraic geometry and algebraic topology.
Research in algebra has often been motivated by observations of the properties of numbers or, more generally, by the properties in number theory, which makes algebra closely related to that theory. On the other hand, research in number theory often involves combinatorial observations or calculations, linking graphs and combinatorics with algebra.
The Algebra Laboratory has the mandate to define the necessary steps to achieve its goal of becoming a reference for theoretical algebra research in rings, modules, number theory, and graphs, as well as collaborating with other fields to develop applied algebra.
Based on these considerations, the areas of interest to be developed need to be explicitly stated as algebraic structures and combinatorics. The study of algebraic structures includes ring theory, module theory, and their extensions, such as semigroups, semirings, coalgebras, and comodules. Meanwhile, combinatorial fields include graph theory, number theory, cryptography, and related fields. Topics related to linear systems and coding theory are areas of applied algebra that are under study and are headed toward applications. In various mathematical modeling techniques, knowledge of matrices and all their peculiarities is essential. Therefore, knowledge of matrix analysis is also a mandatory study for algebra enthusiasts. The Selective Topics course is a platform for studying the latest developments in algebra with topics that are adjusted over time.
In addition to its mission of developing and applying algebra, as part of mathematics in general, a strong foundation in mathematical philosophical thinking is also needed through, among other things, category theory, fuzzy logic, and lattice theory.
Area of Interest in Applied Mathematics and Computing
Applied Mathematics connects mathematical concepts (Algebra, Analysis, Statistics) and techniques with other fields of science or their applications to real-world problems.
The goal of Applied Mathematics research is not only to intelligently apply existing mathematical tools and insights to solve problems but also to develop new theories or methods that can be inspired and driven by real-world applications/problems. Computational technology is essential, both for new methods or applying existing methods to new problems. Computational technology is important for validating new or developed methods by carefully examining the accuracy of estimates and interpreting results, both qualitatively and quantitatively. Therefore, the Applied Mathematics and Computing Interest needs to be established. This area of interest has three types of studies: theoretical studies, numerical studies, and thematic studies. The theoretical study includes four major fields:
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- Field 1: Differential Equations, Dynamical Systems and Bifurcation, and Perturbation Theory,
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- Field 2: Control Theory and Systems Theory,
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- Field 3: Optimization Theory, Game Theory, Operations Research, Fuzzy Programming, Random Fuzzy Programming, and Stochastic Optimization, Queuing Theory, and
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- Field 4: Mathematical Modeling, whether deterministic, probabilistic, or stochastic.
The numerical study is based on computational theory and the development of computational methods and the application of mathematical computation techniques, including Optimization, Ordinary and Partial Differential Equations, Inverse Problems, Machine Learning, Deep Learning, and Big Data.
Thematic studies are based on real-world problems in society, including Cancer Spread Modeling and its Treatment, Healthcare Modeling and Hospital Management, Climate Modeling related to Food Security, Tropical Diseases, and Agricultural Insurance, Biometric Modeling, Applications in Economics, Healthcare, and Traffic Regulation.
These areas of study are integrated into mandatory interest courses, elective courses, and theses. In addition to theoretical or numerical theses, the development of new thematic thesis topics is also possible in the future in response to various problems in society.
Area of Interest in Statistics, Data Science, and Actuarial Science
In general, the interest in Statistics, Data Science, and Actuarial Science relates to modeling and data analysis, designing experiments, making conclusions, predictions, and decisions in the face of uncertainty. The main interest in this field is the application of Statistics; applied problems that drive the development of new methods and the application of advanced Statistical methodologies.
This Statistics interest spans various fields of Statistics, from theoretical to applied studies. Furthermore, this Statistics interest is also interested in developing new Statistical methodologies for complex data, particularly those emerging in fields such as Biology, Financial Statistics, Actuarial Science, and Computational Statistics and Data Science.
- Field of Statistics
This field focuses on the application of probability theory, a branch of mathematics. Specific mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. Areas of work: Lecturers, researchers.
- Field of Actuarial Science
This field uses probability theory, mathematics, statistics, and economics to measure and calculate the financial impact of uncertain future events. Several courses in this field can be used to obtain equivalence for professional actuarial certification from PAI (Persatuan Aktuaris Indonesia). Actuarial Science students can also engage in non-credit internships offered by insurance companies that collaborate with the study program. Actuarial professionals can work in fields such as: Life Insurance, General Insurance, Healthcare, Pension, Employee Benefits, Social Policy, Finance, Investment, and Risk Management.
- Field of Financial Statistics
Financial statistics cover the field of science that analyzes all numerical data that summarizes past behavior or forecasts future behavior of financial security of individuals, a group of securities, or markets in a wide geographical area. Market or industry statistics track the activity of specific securities groups linked by a common trading market or industry classification. Corporate-specific statistics examine the performance of individual companies. Areas of work: Securities markets, financial industry, insurance, investment companies.
- Field of Computational Statistics and Data Science
Computational Statistics is the interface between statistics and computer science. It refers to statistical methods that are enabled by using computational methods. This is a branch of computational science (or scientific computing) specific to mathematical statistics. This area is also rapidly evolving, leading to calls for broader computational concepts to be taught as part of general statistical education.
As in traditional statistics, the goal is to turn raw data into knowledge, but the focus is on computer-intensive statistical methods, such as cases with very large sample sizes and heterogeneous data sets. The terms ‘computational statistics’ and ‘statistical computing’ are often used interchangeably, though some propose distinguishing between them, defining ‘statistical computing’ as “the application of computer science to statistics,” and ‘computational statistics’ as “aiming to design algorithms to implement statistical methods on computers, including those not conceivable before the computer era (e.g., bootstrap, simulation), as well as to tackle analytically difficult problems.” The term ‘computational statistics’ can also refer to computer-intensive statistical methods, including resampling methods, Markov Chain Monte Carlo methods, local regression, kernel density estimation, neural networks, and generalized additive models.
Data science is a discipline specifically studying data, particularly quantitative data (numerical data), whether structured or unstructured. Various subjects discussed in data science include all data processes, from data collection, data analysis, data processing, data management, archiving, data clustering, data presentation, data distribution, to how to turn data into a unified piece of information that everyone can understand.
Data science is a combination of science and social science. The main supporting disciplines in data science consist of mathematics, statistics, computer science, information systems, management, information science, including communication science and library science, archiving, and documentation. Even economics, particularly business science, plays an important role in data science. This field of study uses probability theory, mathematics, statistics, and economics