研究所基本課程介紹
開課時間僅供參考，以實際開課狀況為主。分組修課建議可參考 建議圖| 課程名稱 | 上學期學分 | 下學期學分 |
| 論文研討 | - | - |
| 實變函數論 | 3 | 3 |
| 常微分方程 | 3 | 3 |
| 偏微分方程 | 3 | 3 |
| 離散數學專題 | - | - |
| 偏微分方程數值方法 | 3 | 3 |
| 財務數學導論 | 3 | 3 |
| 密碼學 | 3 | - |
| 有限群表現論 | - | 3 |
| 應用隨機控制 | - | 3 |
| 動態系統專題 | - | 3 |
| 線性規劃 | - | 3 |
| 進階代數 | 3 | - |
| 代數組合學 | - | 3 |
| 演算法 | 3 | - |
| 圖論（圖形學） | 3 | - |
| 代數圖論 | - | 3 |
| 設計理論 | 3 | - |
| 組合學導論 | - | 3 |
| 科學計算導論 | 3 | 3 |
| 應用數學方法 | 3 | 3 |
| 機器學習 | 3 | 3 |
快速連結
研究所課程簡介(點選課程名稱會有更詳盡的介紹)
| 論文研討 |
|---|
| 本課程將定期安排國內外應用數學相關領域的學者至本系演講。透過專家學者的專題報告，讓修課學生能對其研究領域有進一步的認識。...more |
| 實變函數論 |
|---|
| 本課程延續及推廣Riemann積分等微積分相關課程的理論並更進一步了解近代各分析學相關領域的發展，本課程將介紹測度論〈實數線上集合的長度或平面上集合的面積等理論的推廣〉、Lebesgue的積分理論〈Riemann的積分理論的推廣〉以及泛函分析的一些基本理論，作為分析學研究及其它相關應用領域之基礎...more |
| 常微分方程 |
|---|
| 主要為介紹常微分方程的基本性質。大部份的非線性方程式都是無法寫出完整解的。然而，自Poincare 以來，從幾何的觀點，佐以數學分析的刻劃，對非線性方程解的行為及性質，獲致相當之進展。本課程將介紹相關的基本定理與證明；並要求學生能操作解常微分方程基本的軟體計算。...more |
| 偏微分方程 |
|---|
| 本課程屬研究所程度的微分方程課程，授課偏重於數學與物理間的連結，並且讓學生藉由此課程了解直觀地PDE概念。...more |
| 離散數學專題 |
|---|
| 本課程是應用數學研究所組合數學組之必修課程，主要目的在讓本組同學研讀論文並練習上臺報告；但也會安排一些老師來演講。...more |
| 偏微分方程數值方法 |
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| 介紹有限差分法應用於雙曲偏微分方程式與拋物偏微分方程式的數值求解。...more |
| 財務數學導論 |
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| 讓學生了解並熟悉研究財務金融方面所需之數學工具。...more |
| 密碼學 |
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| 讓學生認識密碼學方面的數學工具。
Getting acquainted with the mathematicals tools from cryptography...more |
| 有限群表現論 |
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| Representations and characters of finite groups are very important tools in the group theory. For instance, many proofs in the classification of finite simple groups involve delicate computations in characters. Representation and character theory also has numerous applications in many disciplines, such as number theory, combinatorics, geometry, crystallography in chemistry, and so on. In this course, we will discuss properties of representations and characters of finite groups. Some applications will also be presented....more |
| 應用隨機控制 |
|---|
| 這是一年度共兩學期，介紹應用隨機控制的課程。
This is an one-year introductory course on applied stochastic control. In the first semester, we will start from the basic of stochastic calculus and its applications. In the second semester, applications to optimal stopping and stochastic control will be treated fully for the processes with continuous paths. Some topics in mathematical finance will also briefly be mentioned....more |
| 動態系統專題 |
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| 本門課討論 Patterns Generation 及其相關問題。...more |
| 線性規劃 |
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| 介紹線性規劃的背景由來、數學模型、與其幾類求解線性規劃的方法。...more |
| 進階代數 |
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| 本門課討論為研究所的代數課程。
Abstract Algebra, sometimes also called modern algebra or algebra in short, is the branch of mathematics concerning the study of algebraic structures such as groups, rings, modules and fields. This course is an advanced study of the above structures....more |
| 代數組合學 |
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| This will be a self-contained course focusing on some subjects and methods used in the field of combinatorics....more |
| 演算法 |
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| 本課程是最基本的「計算機科學」之課程之一，目的在學習 “設計演算法” 及 “分析演算法” 的各種技巧，進而明瞭 -- 如何為自己所要解決的問題設計出有效率的演算法，以及分析演算法所使用的資源之多寡。...more |
| 圖論（圖形學） |
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| 這是開給研究生的第一堂圖論課程。
This is the first course of Garph Theory for graduate students. Topics at least include the followings: Trees, Spanning trees and greedy algorithm, Colorings and Chromatic polynomials, Planarity and duality; and some well-known theorems including Cayley Theorem, Turing Graph is the model of many problems, e.g. computer programming, experimental designs, or even pure mathematical problems, and its theory is a delightful playground for the exploration of proof techniques in discrete mathematics. This course prepares students for algorithmic, constructive, probabilistic and algebraic abilities in dealing problems....more |
| 代數圖論 |
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| Algebraic Graph Theory is the branch of mathematics that studies graphs by using algebraic properties of associated matrices. More in particular, spectral graph theory studies the relation between graph properties and the spectrum of the adjacency matrix or Laplace matrix. And the theory of association schemes and coherent configurations studies the algebra generated by associated matrices. This course, also called Linear Algebraic Graph Theory, emphasizes on the first part, and another course, called Algebraic Combinatorics, includes the second part....more |
| 設計理論 |
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| This is a course in the study of combinatorial designs originated from studying the combinatorial structures of experimental designs. Many different designs will be introduced in this one semester course: Latin squares, Steiner systems, t-designs, Hadamard matrices, finite geometries, association schemes and pooling designs. Also, related applications will be mentioned, for example group testing and special networks....more |
| 組合學導論 |
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| 這是研究所組合組必修課，內容涵蓋博士班資格考離散數學考科一半的範圍(另一半為圖論)。...more |
| 科學計算導論 |
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| 科學與工程中的很多問題如氣象預報，金融和經濟的預測和大數據處理等問題是沒辦法使用分析或實證的方式解決，就只能使用電腦模擬的方式來進行研究。此外，利用先進的計算機技術，工業界的產品設計和製造也多依賴於大量的電腦模擬。科學計算作為電腦模擬的核心要素之一, 在每一個模擬計算中，都發揮著很重要的作用，也成為當代科學與技術發展的關鍵角色。本課程的重點是了解和使用科學計算中常用的基礎數值分析與計算方法。能完成這門課程的學生，預計能夠使用計算機模擬來處理：解線性方程組、非線性根發現、優化、曲線擬合、數值積分和微分方程等等的問題。...more |
| 應用數學方法 |
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| 介紹近代應用數學方法的基本知識與工具。
本課程主要目的是去建構、分析並解釋在自然界中物理現象之數學模型，我們將介紹近代應用數學方法的主要構思，並且將問題著重於數學與自然科學間的連結。課程內容包含古典與近代議題，包含量剛分析、regular與irregular擾動方法、變分法、連續體力學等。...more |
| 機器學習 |
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| We introduce the concept of machine learning and several useful learning methods including linear models, nonlinear models, margin-based approaches, structured models, dimension reduction, unsupervised learning (Clustering), ensemble classifiers. Also some special topics and applications will be discussed....more |