{"id":32,"date":"2026-01-18T06:09:36","date_gmt":"2026-01-18T06:09:36","guid":{"rendered":"https:\/\/math-ugm.id\/seamsschool2026\/?page_id=32"},"modified":"2026-02-25T09:08:02","modified_gmt":"2026-02-25T09:08:02","slug":"courses","status":"publish","type":"page","link":"https:\/\/math-ugm.id\/seamsschool2026\/courses\/","title":{"rendered":"Courses"},"content":{"rendered":"\n

1. Measure Theory<\/h2>\n\n\n\n
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Lecturer<\/strong>: Prof. Dr. Christiana Rini Indrati (Universitas Gadjah Mada, Indonesia)<\/p>\n<\/blockquote>\n\n\n\n

This short course provides a structured introduction to measure theory and Lebesgue integration. It begins with the Lebesgue measure on sets of real numbers, exploring measurable and Borel sets, their algebraic properties and characterizations, and the existence of non-measurable sets. The course then discusses measurable functions, their fundamental properties, approximation by simple functions, and key convergence results such as Egoroff\u2019s and Lusin\u2019s theorems. Addressing the limitations of the Riemann integral, it develops the Lebesgue integral for bounded and non-negative functions, framed by essential results including Fatou\u2019s lemma, the monotone and bounded convergence theorems, and the general Lebesgue convergence theorem. Finally, we explore the differentiation of primitives, covering the Vitali covering lemma, functions of bounded variation, the fundamental theorem of calculus, and absolutely continuous functions, underscoring the rich interplay between measure, integration, and differentiation.<\/p>\n\n\n\n

2. Functional Analysis<\/h2>\n\n\n\n
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Lecturer<\/strong>: Eder Kikianty, Ph.D. (University of Witwatersrand, South Africa)<\/p>\n<\/blockquote>\n\n\n\n

This short course offers an introduction to fundamental topics in functional analysis, providing a solid foundation for further study in analysis and applied mathematics. The course begins with normed spaces, completeness, and linear functionals, leading to the Hahn\u2013Banach Theorem and concepts of duality and bounded linear operators. It then covers the Lp spaces and their completeness. <\/p>\n\n\n\n

3. Probability Theory<\/h2>\n\n\n\n
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Lecturer<\/strong>: Dr. Wolfgang Bock (Linnaeus University, Sweden)<\/p>\n<\/blockquote>\n\n\n\n

This short course introduces foundational concepts in probability theory. We begin with Kolmogorov\u2019s axioms and the measure-theoretic framework of probability spaces. Key notions such as random variables, expectation, and independence are developed rigorously. Various modes of convergence are discussed, including almost sure, in probability, and in distribution. Cornerstones are the classical limit theorems: the law of large numbers and the central limit theorem and the Borel-Cantelli lemmas and their applications.<\/p>\n\n\n\n

4. Stochastic Processes<\/h2>\n\n\n\n
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Lecturer<\/strong>: Prof. Dr. Jose Luis da Silva (University of Madeira, Portugal)<\/p>\n<\/blockquote>\n\n\n\n

This is an introductory course to the basic notions of stochastic processes. First, we define the basic objects associated with a stochastic process such as path, distribution, finite dimensional distributions we state the Kolmogorov extension and continuity theorems. We then define and construct some classical stochastic processes such as Brownian motion, Poisson processes, etc., and study their basic properties.<\/p>\n\n\n\n

5. Stochastic Calculus<\/h2>\n\n\n\n
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Lecturer<\/strong>: Prof. Dr. Nicolas Privault (Nanyang Technological University, Singapore)<\/p>\n<\/blockquote>\n\n\n\n

This course will be an introduction to stochastic calculus for continuous diffusion processes. After reviewing the construction and path properties of Brownian motion we will present the construction of the Ito integral and the Ito formula, followed by the stopping time and Girsanov theorems, and the Feynman-Kac formula. Applications will be given to stochastic differential equations, as well as to the construction of Brownian bridges and their score functions, which are used in diffusion-based generative models.<\/p>\n","protected":false},"excerpt":{"rendered":"

1. Measure Theory Lecturer: Prof. Dr. Christiana Rini Indrati (Universitas Gadjah Mada, Indonesia) This short course provides a structured introduction to measure theory and Lebesgue integration. It begins with the Lebesgue measure on sets of…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-32","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/math-ugm.id\/seamsschool2026\/wp-json\/wp\/v2\/pages\/32","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math-ugm.id\/seamsschool2026\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math-ugm.id\/seamsschool2026\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math-ugm.id\/seamsschool2026\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/math-ugm.id\/seamsschool2026\/wp-json\/wp\/v2\/comments?post=32"}],"version-history":[{"count":5,"href":"https:\/\/math-ugm.id\/seamsschool2026\/wp-json\/wp\/v2\/pages\/32\/revisions"}],"predecessor-version":[{"id":97,"href":"https:\/\/math-ugm.id\/seamsschool2026\/wp-json\/wp\/v2\/pages\/32\/revisions\/97"}],"wp:attachment":[{"href":"https:\/\/math-ugm.id\/seamsschool2026\/wp-json\/wp\/v2\/media?parent=32"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}