[全學年]
于靖：Introduction to group representations (1) 李秋坤：環論專題 (2)
[上學期]
蕭欽玉：基本測度論及分佈論 (3) 余正道：代數拓樸 (4)
康明昌：交換代數 (5) 陳其誠：代數數論 (6)
鄭日新：Geometry of several complex variables (7) 李元斌：量子上同調入門 (8)
張志中：隨機過程導論 (9)
王偉仲／陳素雲／陳君厚：資料科學之計算方法與工具 陳俊全：演化動力學 (10)
王藹農：極小曲面 (11) 陳宏：統計計算 (12) [下學期]
林長壽：複分析 II (13) 陳君明：密碼學導論 王金龍：D 模 (14)
李元斌：量子上同調專題 (15) 張樹城：瑞曲流 II (16)
蕭欽玉：柯西黎曼流形上的分析與幾何 (17) 林大溢：大數據理論及實務應用 (18)
韓傳祥：數理金融導論 黃信誠：統計學習 (19) 王偉仲：數學軟體 (20) 江金倉：廣義線性模型
王振男／林太家：Special topics of PDE and its applications 黃啟瑞：隨機微機分
[暑期密集課程]
為鼓勵學生參加 NCTS 暑期課程，今年暑假將開設3 門暑期短期密集的課程作
為台大數學系的正式課程
（有學分數）
Course Description
Department of Mathematics
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Introduction to Group Representations.
Contents.
We introduce group representations for finite groups, compact groups, and locally compact groups. The later includes p-adic groups, adelic groups, i.e
. automorphicrepresentat_ions of algebraic groups over global fields. We will use algebraic tools primarily. But we will also bring in tools from harmonic analysis, Haar integrals, complex analysis
, and distribution theory. We will do classification of representationsfor classes of groups. Will also apply representation theory to problems arising and connected with other fields of mathematics, particularly number theory and arithmetic geometry.
Course Goal.
Representations of groups play a central role in mathematics. Great progress had been made in the last century which lead to solutions of many key problems in
mathematics
. Currently, the developments ofrepresentation theory of groups involves
most active frontier researches. Our goal i'S to introduce students this very important
field
. This course is suitable for advanced undergraduates as well as beginninggraduate students.
Itconnects all the basic courses, algebra and analysis.
Itunderlines
to students the fact that combining all the fundamental tools previously learnt is
essential for doing modern mathematics researches.
Nature of the course 0 required 0 elective Calculus 0 Calculus A Course number
Course title Instructor
I. *Contents :
II. Course prerequisite :
Course Description
~partment of Mathematics
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Department of Mathematics
Nature of the course
required
elective
分析Calculus Calculus A Calculus B
Course number Section number 免填 Number of credits 2
Course title 課 程 名 稱 ： 基本測度論及分佈論 (Basic measure theory and distribution theory)
Instructor 教授： Chin-Yu Hsiao 蕭欽玉 I. ＊Contents：
[I] A review of differential calculus in Euclidean space [II] Lebesgue measure in Euclidean space.
[III]Lebesgue integral in Euclidean space.
[IV] $L^ p$ spaces in Euclidean space.
[V] The Fubini theorem.
[VI]Test functions, convolution, cutoff functions and partitions of unity.
[VII] Definition and basic properties of distributions.
[VIII] Applications of distribution theory
II.
Course prerequisite：
高微, 線代.
III. ＊Reference material ( textbook(s) )：
自編講義.
IV. ＊Grading scheme：請填寫各項計分之百分比，例如：期中 30% 期末 40% 作業 10% 報告 20%，總計 10
V. 期中:%, 30 期末:40% 作業:30%
VI. ＊Course Goal：
這是一門專為大學部修過高微的學生開的分析課程.. 測度論是近代分析學最基本的工具.
這們課第一部份將會仔細的介紹歐式空間的測度論; 我將在不預設太多的預備知識下, 儘量讓學生
了
解歐式空間中的測度論. 希望上完這門課的測度論之後, 學生更容易接受研究所的實分析課程.
這門課的第二部份將會仔細的介紹基本的分佈論(distribution theory). Distribution 的概念由法國數學 家 Laurent Schwartz 在 1940 年代引入. 現代的
distribution theory 基乎是近代 PDE, Harmonic analysis, Fourier analysis 甚至 Geometric analysis 的基礎.
上完基本測度論後, 我會介紹最基本的 Distribution Theory 並由 Distribution Theory 的觀點來處理之 前就學過的分析題材, 如 GaussGreen formula, Stoke formula, Cauchy integral formula, Weierstrass theorem 及古典的 potential theory. 希望上完這門課的分佈論之後, 學生更容易接受研究所的 PDE, Harmonic analysis, Fourier analysis 等課程.
這門課, 我之前有開過, 當時是三學分, 現雖為兩學分, 但我會努力的把上課內容作到和之前的課一 樣. 此外, 和之前的課不一樣的地方在於, 今年我會更強調習題. 除了正課外, 希望每週會有一小時 的習題課.
1. ＊號為必填欄位
2. 大綱內容字數英文最少 200 字以上
3
Course Description
Department of Mathematics
Nature of the course: Elective Area : 幾何與拓樸
Course number Section number 免填 Number of credits 3 Course title 課程名稱：代數拓樸 (Algebraic Topology)
Instructor 教授： 余正道
I. ＊
Contents : 1. Homology 2. Cohomology 3. Fundamental group 4. Sheaves in topology
II.
Course prerequisite :
Familiar with basics of pointset topology (e.g. touched in Introduction to Analysis)
III. ＊
Reference material (
textbook (
s ) ):
Hatcher,
Algebraic topology. Dimca,
Sheaves in topology.
IV. ＊
Grading scheme :
Homework assignments (40%), midterm (30%), oral presentation (30%)
V. ＊
Course Goal :
The languages, ideas and tools emerged from algebraic topology have become indispensable in all areas
of mathematics. One aim of this course is to provide a quick and intense introduction to important contents in algebraic topology. The final part is to go into the theories of categories and sheaves. The goal is to prepare students with working knowledges in algebraic topology, which are impartant in modern developments in geometry, e.g., in the study of singular spaces.
2
C o u r s e D e s c r i p t i o n
Department of Mathematics
Nature of the course
required elective
Area 麻煩老師勾選類別，或直接填寫 。
代數與數論 分析 幾何與拓樸 計算與應用數學
機率 統計 離散數學 其他 論文研討、獨立研究 Calculus Calculus A Calculus B
Course number Section number 免填 Number of credits Course title 課程名稱： Commutative Algebra
Instructor 教授：
I. ＊Contents：Localization, integral extension, differentials, smooth morphisms
II. Course prerequisite：
Algebra I,II
III. ＊Reference material ( textbook(s) )：
Atiyah and MacDmald, Introduction to commutative algebra Matsumma, Commutative ring theory
Hartshorne, Algebraic geometry
IV. ＊Grading scheme：請填寫各項計分之百分比，例如：期中 30% 期末 40% 作業 10% 報告 20%，總計 100%
Homework, 20%
Final examination, 80%
V. ＊Course Goal：
We will discuss the notion of localization, integral extensions and dimensions of commutative rings. Then we recall sheaves of modules on a scheme. In particular, we will introduce the sheaves if differentials and non-singular varieties.
If the time permits, we will study flat morphisms and smooth morphisms.
1. ＊號為必填欄位
2. 大綱內容字數英文最少 200 字以上
5
C o u r s e D e s c r i p t i o n
Department of Mathematics
Nature of the course
required elective
Area 麻煩老師勾選類別，或直接填寫 。
代數與數論 分析 幾何與拓樸 計算與應用數學
機率 統計 離散數學 其他 論文研討、獨立研究 Calculus Calculus A Calculus B
Course number Section number 免填 Number of credits 3 Course title 課程名稱： algebraic number theory
Instructor 教授： Ki-Seng Tan
I. ＊Contents：Algebraic Numbers, Algebraic Integers, Dedekind Domain, Class Groups, Units, Class Number Formula, Density Theorem.
II. Course prerequisite Introduction to Algebra
III. ＊Reference material ( textbook(s) )：M. Murty ``Problems in Algebraic Number Theory”
IV. ＊Grading scheme：請填寫各項計分之百分比，例如：期中 30% 期末 40% 作業 10% 報告 20%，總計 100%
To be determined.
V. ＊Course Goal：To introduce to students the number theory developed (mainly) in the 19th century.
1. ＊號為必填欄位
2. 大綱內容字數英文最少 200 字以上
C o u r s e D e s c r i p t i o n
Department of Mathematics
Nature of the course
required elective
Area 麻煩老師勾選類別，或直接填寫 多複變幾何分析。
代數與數論 v分析 v幾何與拓樸 計算與應用數學
機率 統計 離散數學 其他 論文研討、獨立研究 Calculus Calculus A Calculus B
Course number Section number 免填 Number of credits 3 Course title 課程名稱： Geometry of Several Complex Variables
Instructor 教授： Jih-Hsin Cheng
I. ＊Contents：
Basic theory of several complex variables (SCV), Geometry of boundary of a complex domain, positive mass theorem, Levi mean curvature, p-mean curvature, Alexandrov-type problem, isoperimetric problem in Heisenberg group, flows of CR structure, local embedding problem, index formula.
II. Course prerequisite：
Theory of one complex variable, Basic differential geometry, Basic elliptic PDE (preferred).
III. ＊Reference material ( textbook(s) )：
Relevant books and papers, e.g., So-Chin Chen and Mei-Chi Shaw’s book on SCV, Howard Jacobowitz’s book on CR structures, Cheng-Malchiodi-Yang’s paper on CR positive mass theorem, Cheng-Hsiao-Tsai’s paper on local index formula for CR manifolds with S^1 action, my other papers (with Jenn-Fang Hwang, Hung-Lin Chiu, Andrea Malchiodi, and Paul Yang) on p-mean curvature equation, etc..
IV. ＊Grading scheme：請填寫各項計分之百分比，例如：期中 30% 期末 40% 作業 10% 報告 20%，總計 100%
Homework: 80%
Report (oral or written): 20%
V. ＊Course Goal：
I expect that students can start working on some research problems in this field after the course.
1. ＊號為必填欄位
2. 大綱內容字數英文最少 200 字以上
7
Nature of the course
0 required ~X elective Calculus 0 Calculus A
Course Description
Department of Mathematics
Area .lffi~~OiP1;J:l!~JJ1J, !!Xll.-ti:J:}~~:F,J Algebraic Geometry.
0 Algebra 0 Analysis ~X Geometry 0 Statistics 0 Applied Mathematics 0 Discrete Mathematics 0 Others 0 Calculus B
Course number
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Number of creditsI
4Course title ~l~J~~flf(~X) Introduction to Gromov-Witten theory Instructor ~1~ Y.P. Lee
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*Contents: This is the first semester of a 2-semester sequence of course in Gromov--Witten theory.
Possible topics includes
•
•
•
•
Moduli of curves and maps . Virtual fundamental cycles .
Equivariant cohomology/intersection theory. (Virtual) localization . Givental's formulation .
The format of this class is to have 2 hours of lectures and 2 hours of student seminar each week. The lecture should cover the basics of GW theory. However, since the GW theory requires a lot of preparatory material, it would not be productive to teach it during the regular lectures. Instead, the students will be required to present the assigned material in turns (and in English, although the language will be discussed among the participants). The potential benefits of this approach are manifold. Not only would the students learn better, but I also get to know the students better. Furthermore, this way the lectures can move at a brisk pace while the background material will be discussed in details during the student seminars.
Course prerequisite: Basic algebraic geometry and topology.
*Reference material ( textbook(s) ): No textbook. The material will be assigned throughout the semester.
*Grading scheme: iiJ.,:!:fU.&~J~~t7tZ.. IT
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20%, ~-fit 100%.No exam. The grades arc decided by the presentation in the seminars and performance in the class.
Others:
*Course Goal: To learn the basics ofGromov--Witten theory.
1.
*
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elective D Algebra D Analysis D Geometry D Statistics D Applied Math. D Discrete Math. 0 Probability Calculus 0 CalculusA D Calculus BCourse number 221 U441 0
I
Section number1 j
Number of credits j 3Course title INTRODUCTION TO STOCHASTIC PROCESSES Instructor CHIH-CHUNG CHANG ~;0cp
1. Contents: martingales, discrete-time Markov chains, and Poisson processes.
2. Course prerequisite: elementary probability theory, linear algebra, and advanced calculus.
3. Reference material (textbook(s)):
(a) Markov chains and mixing times. By D. A. 'Levin, Y. Peres, and E. L. Wilmer. AMS 2008
0
Xa) Introduction to stochastic processes. By G. F. Lawler. Chapman & Hall/CRC, 2nd edition.(, (o) Essentials of stochastic processes. By R. Durrett, Springer, 1999.
(~ '(c.) An Introduction to Markov Processes. By D. W. Stroock. Springer, 2005.
4. Grading scheme:
Recitation, homework, oral presentation, and final exam.
(a ?'\L-11""~)
5. Course Goal: Learn the skill to model, and the technique to analyze, the random phenomena evolving with time. , ... ,.J; , .( _-, , ~ 1 ~ -..
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9
C o u r s e D e s c r i p t i o n
Department of Mathematics
Nature of the course
required elective
Area 麻煩老師勾選類別，或直接填寫 。
代數與數論 分析 幾何與拓樸 計算與應用數學
機率 統計 離散數學 其他 論文研討、獨立研究 Calculus Calculus A Calculus B
Course number Section number 免填 Number of credits 2 Course title 課程名稱：演化動力學(Evolutionary Dynamics)
Instructor 教授： 陳俊全
I. ＊Contents：
Evolution is a central theme in biology. It is also very important in agricultural, medical, and social sciences.
The course introduces basic mathematical principles in evolutionary dynamics and the issue how
cooperation emerges among selfish individuals. The contents cover the Nash equilibrium, evolutionarily stable strategy, social dilemmas of cooperation, effects of direct and indirect reciprocity, models involving reputation, and rewards and punishment in the maintenance of cooperation.
II. Course prerequisite：
Linear algebra, calculus, ordinary differential equations.
III. ＊Reference material ( textbook(s) )：
Karl Sigmund: The Calculus of Selfishness, Princeton University Press, 2010.
IV. ＊Grading scheme：請填寫各項計分之百分比，例如：期中 30% 期末 40% 作業 10% 報告 20%，總計 100%
V. ＊Course Goal：
The course introduces basic concepts in evolutionary game dynamics.
1. ＊號為必填欄位
2. 大綱內容字數英文最少 200 字以上
,' j
r { \•r
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~
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Contents
Preface.
1 Introduction. 1
2 Basic results in classical minimal surface theory. 11 2.1 Eight equivalent definitions of minimality. 11 2.2 Weierstrass representation. . . 15
2.3 Minimal surfaces of finite total curvature. 17
2.4 Periodic minimal surfaces. . . 19 2.5 Some interesting examples of complete minimal surfaces. 20 2.6
2.7 2.8 2.9
::vionotonicity formula and classical maximum principles. 30 Ends of properly embedded minimal surfaces. . . 33 Second variation of area, index of stability and Jacobi functions. 35 Barrier constructions. . . . . . . . 39 3 Minimal surfaces with finite topology and more than one
end. 43
3.1 Classification results for embedded minimal surfaces of finite total curvature. . . . . 43 3.2 Constructing embedded minimal surfaces of finite total cur-
vature. . . . . . . . . . . . . . . . . . . . . . 44 4 Sequences of embedded minimal surfaces with no local area
bounds. 51
4.1 Colding-Minicozzi theory (locally simply-connected). 51 4.2 Minimal laminations with isolated singularities. . . . 59
11
IV
5 The structure of minimal laminations of JR3.
6 The Ordering Theorem for the space of ends.
7 Conformal structure of minimal surfaces.
7.1 Recurrence and parabolicity for manifolds.
7.2 Universal superharmonic functions . . . . 7.3 Quadratic area growth and middle ends . . 8 Uniqueness of the helicoid I: proper case.
Preface.
63 67 71 71
74 76 81 9 Embedded minimal annular ends with infinite total curva-
ture. 85
9.1 Harmonic functions on annuli. . . 85 9.2 Annular minimal ends of infinite total curvature. 87
10 The embedded Calabi-Yau problem. 95
10.1 Uniqueness of the helicoid II: complete case. . . 95 10.2 Regularity of the singular sets of convergence of minimal lam-
inations. . . 98 11 Local pictures, local removable singularities and dynamics.105 12 Embedded minimal surfaces of finite genus.
12.1 The Hoffman-Meeks conjecture . . . . 12.2 Nonexistence of one-limit-ended examples .. . 12.3 Uniqueness of the Riemann minimal examples.
12.4 Colding-Minicozzi theory (fixed genus).
13 Topological aspects of minimal surfaces.
14 Partial results on the Liouville Conjecture.
15 The Scherk Uniqueness Theorem.
16 Calabi-Yau problems.
17 Outstanding problems and conjectures.
117 117 119 122 127 131 141 145 149 153
C o u r s e D e s c r i p t i o n
D e p a r t m e n t o f M a t h e m a t i c s
Nature of the course
required elective
Area
Algebra Analysis Geometry Statistics
Applied Mathematics Discrete Mathematics Others Calculus Calculus A Calculus B
Course number 221 U2000 Section number Number of credits 3 Course title 統計計算 STATISTICAL COMPUTING
Instructor Hung Chen 陳宏 I. Contents:
1 Simulation Methodology
2 Monte Carlo methods for statistical inference: Maximum Likelihood Estimation and EM algorithm; bootstrapping; cross validation
3 Nonlinear regression and optimization
3 Numerical methods in statistics ("statistical computing")
4、Applications to Parametric Statistics: linear regression and least squares (using numerical linear algebra); generalized linear models (using numerical optimization); iteratively reweighted least squares and generalized linear models; Lasso (using convex optimization)
5、Applications to Nonparametric Statistics and beyond: density estimation (kernel density estimation, choice of bandwidth); regression function estimation ( spline smoothing, computation of splines using numerical linear algebra, principle component analysis using numerical linear algebra)
II. Course prerequisite：Calculus, one semester of linear algebra or equivalent, Mathematical Statistics such as Statistics offered at Math department, some programming experience preferred.
III. 課程目標: To make the computational statistics techniques available to a wide range of users including statisticians, engineers and scientists. We will discuss motivations, contents, approaches, applications and computation codes.
IV. Reference material ( textbook(s) )：
Lecture notes, slides, reference material will be posted on course web IV. Grading scheme：
作業 30%, 計畫報告: 20%, Quizzes: 20%, Midterm: 30%
V. Others: Hung Chen e-mail: [email protected] Course Goal：
1. To understand and be able to use probability as the language of uncertainty.
2. To read statistical arguments critically.
3. To see how statistics is done in Science, Medicine, Education, Business, Government, Law, Politics, and other fields.
4. To think in probabilistic terms in dealing with risk in our daily lives.
5. To familiar with one statistical software.
12
Nature of the course 0 required
I
electiveCalculus
0
Calculus ACourse Description
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C o u r s e D e s c r i p t i o n
Department of Mathematics
Nature of the course
required elective
Area 麻煩老師勾選類別，或直接填寫 。
代數與數論 分析 幾何與拓樸 計算與應用數學
機率 統計 離散數學 其他 論文研討、獨立研究 Calculus Calculus A Calculus B
Course number Section number 免填 Number of credits 3 Course title 課程名稱： D Modules
Instructor 教授： 王金龍 I. ＊Contents：
I will introduce D modules with emphasizes on the functorial properties. Then I will discuss specific examples including quantum D modules and Hodge—Stokes structures.
II. Course prerequisite：
Basics in differential geometry, algebraic topology, and algebraic geometry in the level of Hartshorne’s textbook chapter 2 and 3.
III. ＊Reference material ( textbook(s) )：
[1] Ginzburg: Lectures on D modules (1998 Chicago lectures).
[2] Sabbah: Introduction to Stokes structures, Springer 2013.
IV. ＊Grading scheme：請填寫各項計分之百分比，例如：期中 30% 期末 40% 作業 10% 報告 20%，總計 100%
No exams. Midterm and Final scores are based on presentations of assigned material.
V. ＊Course Goal：
Many recent advances on Riemann—Hilbert correspondences, integrable systems, quantum cohomology, and mirror symmetry via refined study of Gauss—Manin connections require the machinery of D modules in an essential way.
The goal of this course is however modest. I plan to prepare the fundamental part of the D modules theory, especially on the six operations in the derived category of D modules. I will also discuss several examples towards recent researches.
It is expected that participants of this course will get enough background to read more advanced topics through assigned presentations.
1. ＊號為必填欄位
2. 大綱內容字數英文最少 200 字以上
14
Nature of the cour~
0 required
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elective Calculus D Calculus ACourse Description
Department of Mathematics
Area Jff~~~§rp~~;f~)71j, E)t]§Ji±J'i~ Algebraic Geometryo 0 Algebra 0 Analysis
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Geometry 0 Statistics0 Applied Mathematics 0 Discrete Mathematics 0 Others D Calculus B
Course number
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Section numberI ~:l:ft I
Number of credits14
Course title aJ~!6lfli(~Jt) Topics in Gromov-Witten theory Instructor
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* Contents: This is the second semester of a 2-semester sequence introductory course in Gromov-- Witten theory. Possible topics includes
•
•
•
•
Relative Gromov--Witten theory and degeneration formula . Orbifold Gromov--Witten theory .
Quasimap theory .
Donaldson--Thomas theory and other flavors of Gromov-Witten-like theory .
The format of this class is to have 2 hours of lectures and 2 hours of student seminar each week. The lecture should cover the basics ofGW theory. However, since the GW theory requires a lot of preparatory material, it would not be product to teach it during the regular lectures. Instead, the students will be required to present the assigned material in turns (and in English, although the language will be discussed among the participants). The potential benefits of this approach arc manifold. Not only would the students learn better, but I also get to know the students better. In the future, if the students plan to apply for graduate study, I will be able to write convincing letters for them. Furthermore, this way the lectures can move at a brisk pace while the background material will be discussed in details during the student seminars.
Course prerequisite: Basic algebraic geometry and topology. Successful completion of the first semester.
*Reference material ( textbook(s) ): No textbook. The material will be assigned throughout the semester.
*Grading scheme: ~l'Jtlii.-5-&Jfi,Jt5tZ.IT7Ht. {§IJ~D: ~l-j-1 30% WPi~ 40% ft~ 10% *Fr4· 20%, ~;;t 100%.
No exam. The grades are decided by the presentation in the seminars and performance in the class.
Others:
*Course Goal: To learn selected advanced topics in Gromov--Witten theory.
1. *
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The Ricci Flow II
學期 105-2
授課對象 數學系 數學所
課號 MATH
班次
學分(數) 3
必/選修 選修 選修
教師 張樹城
全/半年 半年
上課時間 星期三 345
上課地點 TIMS103
課程大綱
課程概述
1. Tensor calculus 2. Kaehler geometry
4. The Ricci flow on Kaehler manifolds
課程目標 Shall be able to do research in this direction.
關鍵字 Ricci flow, kaehler Ricci flow
課程要求 Need some preliminary of the Ricci flow on Riemannian manifolds.
指定閱讀
參考書目 J. Song and B. Weinkove, Lecture notes on the Kaehler-Ricci flow
面談時間 另約時間
16
C o u r s e D e s c r i p t i o n
Department of Mathematics
Nature of the course
required
elective
分析, 幾何與拓樸 Calculus Calculus A Calculus BCourse number Section number 免填 Number of credits 3
Course title 課程名稱： Analysis and Geometry on CR manifolds (科西黎曼流形上的分析與 幾何)
Instructor 教授： Chin-Yu Hsiao 蕭欽玉 I. ＊Contents：
(I)An introduction to CR manifolds (II)An introduction to Kohn Laplacian
(III) Kohn-Hormander's L^2 estaimates for Kohn Laplaican
(IV) An introduction to Microlocal Analysis: Pseudodifferential operators and Fourier integral operators (V) An introduction to Microlocal Analysis: Complex Fourier integral operators
(VI) Microlocal analysis for Kohn Laplacian
(VII) Boutet de Monvel-Sjostrand's theorem for Szego kernel and Fefferman's theorem for Bergman kernel (VIII) Analysis and Geometry on CR manifolds with S^1 action
(IX) From CR geometry to Complex geometry. Deduce Kodaira vanishing Theorem, Kodaira embedding theorem, Tian-Yau-Zelditch asymnptotic exopansion.
II.
Course prerequisite：
Differential Geometry, P.D.E, real analysis.
III. ＊Reference material ( textbook(s) )：
自編講義.
IV. ＊Grading scheme：請填寫各項計分之百分比，例如：期中 30% 期末 40% 作業 10% 報告 20%，總計 10
V. 期中:25%, 期末:25% 報告:50%
VI. ＊Course Goal：
科西黎曼流形是非常重要的一類流形, 在數學物理上伴演著重要角色. 最基本的例子就是複流形的邊 界及一個解析線叢(holomorphic line bundle)的 circle bundle. 許多複幾何的結果都可從科西黎曼流 形上的結果得到. 科西黎曼流形上的研究, 最困難的地方就是處理的算子 Kohn Laplacian 是一個非橢 圓的算子, 甚至在許多情形下, 連次橢圓性都缺乏(non-hypoelliptic operator). 這門課除了介紹基本
的科西黎曼流形外, 還會介紹如何利用現代分析的工具來處理 Kohn Laplacian, 及利用這些現代分析 的工具來處理一些幾何問題. 若時間足夠, 我還會談談如何從 Kohn Laplacian 的解出發, 得到複幾何 的幾個經典結果.
1. ＊號為必填欄位
2. 大綱內容字數英文最少 200 字以上
17
C o u r s e D e s c r i p t i o n
Department of Mathematics
Nature of the course required elective
Area 麻煩老師勾選類別，或直接填寫 。
代數與數論 分析 幾何與拓樸 計算與應用數學
機率 統計 離散數學 其他 論文研討、獨立研究
Calculus Calculus A Calculus B
Course number Section number 免填 Number of credits 3
Course title 課程名稱：大數據理論及實務應用
Big Data Applications and Theories
Instructor 教授：林大溢
I. ＊Contents：
1.What is Big Data?
2.Google Tools and Big Data 3.TED and Big Data Cases
4.Big Data Research methods I 5.Big Data Research methods II
6.Taiwan Big Data sources and applications cases I 7.Taiwan Big Data applications cases II
8.USA Big Data applications cases I 9.USA Big Data applications cases II 10.USA Big Data applications cases III 11.UK Big Data applications cases 12. Japan Big Data applications cases
13. Australia Big Data applications cases
14.Global Business and industry applications cases 15.Big Data Challenges and Trends
II.
Course prerequisite：
III. ＊Reference material ( textbook(s) )：
1. Open Data Now: The Secret to Hot Startups, Smart Investing, Savvy Marketing, and Fast Innovation
2. All You Can Pay: How Companies Use Our Data to Empty Our Wallets(失控的大 數據)
3. BUSINESS INTELLIGENCE AND ANALYTICS: FROM BIG DATA TO BIG IMPACT
4. Big Data: The Management Revolution, Andrew McAfee and Erik Brynjolfsson
IV.
V. ＊Grading scheme：
VI.
上台報告 40% ，期中報告 30% ，期末報告 30% ，總計 100%VII. ＊Course Goal：
To introduce students to know what and how about big data
1. ＊號為必填欄位
2.
大綱內容字數英文最少 200 字以上
18
Syllabus: Spring 2017 統計學習 (Statistical Learning) Textbook and Reference
Hastie T, Tibshirani R and Friedman J (2009). The Elements of Statistical Learning,
Data Mining, Inference and Prediction. Springer, 2nd edition.
James G, Witten D, Hastie T, Tibshirani R (2013). An Introduction to Statistical
Learning with Applications in R. Springer.
Objectives
This course will introduce various statistical techniques for extracting information from data. Students taking this course are expected to have a working knowledge of using these techniques in practice.
Course Outline
1. Introduction & overview 2. Linear methods for regression
‧ Linear regression
‧ Classical model selection methods
‧ Shrinkage methods, penalized regression 3. Linear methods for classification
‧ Linear discriminant analysis
‧ Logistic regression 4. Nonparametric models
‧ Basis expansion, regularization, splines
‧ Generalized additive models
5. Tree-based methods, ensemble methods
‧ Classification trees, regression trees, random forest
‧ Multivariate adaptive regression splines
‧ Boosting and bagging 6. Support vector machines 7. Unsupervised learning
‧ Cluster analysis
‧ Principal component analysis
Course Prerequisites
Introductory statistics, introductory probability theory, linear algebra, and some programming background in using R.
Grading
Homework (60%)
Project (40%)
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1
課程大綱調查表
I. Contents：
本課程採用「做中學」以及「翻轉教室」的教學策略，透過多個實例單元以線上教學、講課、實作、討 論與合作學習等方式進行教學。課程有下列三大主軸。
一、基本 MATLAB 程式語言（前半學期）
此部分將以翻轉教室的方法進行。主要目的是介紹 MATLAB 程式語言，以及如何使用 MATLAB 解決 數學問題。
二、培養與精熟問題解決，演算法開發，與程式寫作等能力。（後半學期）
課堂中將進行數個學習單元，每個學習單元包含 (1) 動機問題鋪陳 （取材自科學、工程、生物、社會科 學等應用），(2) 演算法發展與相關 MATLAB 語法，(3) 程式寫作與除錯，(4) 計算結果詮釋及其數學與 科學意涵探究。
三、小組計畫（整學期）
主要目的是整合與應用課堂所學，增進跨領域的視野與理解，嘗試創新的思考，並培養規劃與實踐計畫 課 程 名 稱
（中文） 數學軟體
（英文） Mathematical Software
課 程 所 屬 領 域
（ 請 勾 選 ）
代數 分析 幾何 離散
統計 機率或金融 計算或應數
課 程 規 劃
（ 請 勾 選 ）
學年課
學期課 ：上學期 下學期
開課對象：大學部 (一年級以上)
研究生
上課時間： 預估修課人數：
2
的能力。
II. Course Goal：
- 能理解動機問題
- 能對問題解決進行概念性的抽象思考，產生邏輯性的解決方案（演算法）
- 能將演算法具體化，以 MATLAB 實作程式
- 能透過除錯與數值實驗方式，將演算法與程式發展得更嚴謹與更有效率。
- 增進計算科學的基本素養（包含離散化、維度、趨近、資料視覺化、隨機、與複雜度）
- 透過程式與數學的交互作用，加強利用數值計算與幾何圖形進行推理的能力 - 能對科學，數學，電腦計算有跨領域的整體觀與思維
- 培養口語溝通與表達能力 - 培養合作、創造與寫作能力
II. Course Prerequisite：
本課程不要求學生具備程式能力，但應有主動積極的學習態度。將用到部分微積分，線性代數。
III. Reference Material (textbook(s) )：
[1] An Interactive Introduction to MATLAB (www.see.ed.ac.uk/teaching/courses/matlab/)
[2] Data-Driven Modeling & Scientific Computation: Methods for Complex Systems and Big Data Paperback (2013), J. Nathan Kutz
[3] Coding the Matrix: Linear Algebra through Applications to Computer Science Paperback (2013), Philip N.
Klein
[4] Insight Through Computing: A MATLAB Introduction to Computational Science and Engineering (2010), by Charles F. Van Loan and K.-Y. Daisy Fan.
[5] “A Matlab Companion for Multivariable Calculus” by Jeffery Cooper. ISBN-13: 978-0121876258 [6] MATLAB 程式設計 [入門篇]，張智星
[7] Experiments with MATLAB, by Cleve Moler, 2009 (www.mathworks.com/moler/exm/index.html) [8] MATLAB Guide (2nd edition) by Desmond J. Higham and Nicholas J. Higham
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3
(www.see.ed.ac.uk/teaching/courses/matlab/) [9] 課堂中提供講義
IV. Grading Scheme：
課堂中作業 20%，小組學期作業 20%，期中考 30%，期末考 30%
