POSTGRADUATE PROGRAM (MAGISTER) Kompetensi Lulusan

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1 [FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM]

[FACULTY OF MATHEMATICS AND NATURAL SCIENCES]

Program Studi

Department

[JURUSAN MATEMATIKA]

[MATHEMATICS DEPARTMENT] Jenjang Pendidikan

Programme

PROGRAM PASCA SARJANA (MAGISTER)

POSTGRADUATE PROGRAM (MAGISTER)

Kompetensi Lulusan

x AKADEMISI DI BIDANG MATEMATIKA DAN TERAPANNYA

x PENELITI DI BIDANG MATEMATIKA DAN TERAPANNYA

Graduate Competence

x ACADEMICIAN IN MATHEMATICS AND ITS APPLICATIONS

x RESEARCHER IN MATHEMATICS AND ITS APPLICATIONS

STRUKTUR KURIKULUM/

COURSE STRUCTURE

No. Kode MK Code

Nama Mata Kuliah (MK) Course Title

sks Credits SEMESTER I

1 SM092301 Aljabar

Algebra

3

2 SM092303 Analisis Fungsional

Functional Analysis

3

3 SM092305 Pemodelan Matematika dan Simulasi

Mathematical Modeling and Simulation

3

4 SM092307 Bioinformatika

Bioinformatics

3

Jumlah sks/Total of credits 12

SEMESTER II

1 SM092302 Komputasi Numerik

Numerical Computation

3

2 SM092304 Komputasi Jaringan Syaraf Tiruan

Artificial Neural Network Computation

3

3 Mata Kuliah Pilihan

4 SM092202 Optimasi Dinamis

Dynamics Optimazation

3

5 SM092204 Logistik dan Metode Perencanaan Transportasi

Logistics and Transportation Planning Method

3

6 SM092206 Teori dan Aplikasi Graf

Theory and Application of Graph

3

7 SM092208 Dispersi Atmosfir

Atmospheric Dispersion

3

8 SM092210 Kecerdasan Buatan

Artificial Intelegence

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SEMESTER III

1 SM092201 Aljabar MaxPlus

MaxPlus Algebra

3

2 SM092203 Komputasi Dinamika Fluida

Computational Fluid Dynamics

3

3 SM092205 Kontrol Optimum

Optimum Control

3

4 SM092207 Kapita Selekta Pemodelan dan Simulasi

Special Topic of Modeling and Simulation

3

5 SM092209 Analisis Wavelet

Wavelet Analysis

3

6 SM092211 Kapita Selekta Analisis Terapan

Special Topic of Applied Analysis

3

7 SM092213 Multikriteria Optimum

Optimum Multicriterion

3

8 SM092215 Analisis Time Series

Time Series Analysis

3

9 SM092217 Teori Resiko dan Analisis Keputusan

Risk Theory and Decision Analysis

3

10 SM092219 Sistem Fuzzy

Fuzzy System

3

11 SM092221 Pengolahan Citra

Image Processing

3

12 SM092223 Analisis Data Survival

Data Survival Analysis

3

13 SM092225 Optimasi Heuristik

Heuristic Optimazation

3

14 SM092227 Optimasi Kombinatorial

Combinatorial Optimazation

3

15 SM092229 Kapita Selekta Riset Operasi

Special Topic of Operation Research

3

16 SM092231 Grid Computing

Grid Computing

3

17 SM092233 Data Mining dan Pengenalan Pola

Data Mining and Pattern Recognition

3

18 SM092235 Kapita Selekta Ilmu Komputer

Special Topic of Computer Science

3

19 SM092237 Invers Problem

Invers Problem

3

20 SM092239 Riset Operasi Lanjut

Advanced Operation Research

3

Jumlah sks/Total of credits 12

SEMESTER IV

1 SM092306 Tesis

Thesis

6

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PROGRAM PASCASARJANA/MAGISTER PROGRAM

SILABUS KURIKULUM/COURSE SYLLABUS

MATA KULIAH/

COURSE TITLE

Semester: I

TUJUAN

PEMBELAJARAN/

LEARNING OBJECTIVES

x Mahasiswa mampu memahami secara umum struktur aljabar dan notasinya.

x The Students will be Understand to the generalize of the structures algebra and related notion.

KOMPETENSI/ COMPETENCY

x Mahasiswa mampu menerapkan aljabar dalam matematika dan masalah riil

x The students be able to apply algebra in the mathematics and real problems

x Mahasiswa mampu menganalisis struktur aljabar x The students able to analyze the structure algebra. x Mahasiswa mampu menyusun contoh-contoh aplikasi x The studentds able to contruct some application exsamples POKOK

BAHASAN/ SUBJECTS

x Grup dan semigrup x Grup and Semigrup

x Field berhingga dan Polinomial x Finite field and Polynomial

PUSTAKA UTAMA/ REFERENCES

Spindler K., Abstract Algebra With Applications, Volume I Macmilan Marcel Dekker.Inc, 1994

Spindler K., Abstract Algebra With Applications, Volume II Macmilan Marcel Dekker.Inc, 1994.

Lidl R, and G. Pliz, Applied Abstract Algebra: Second Edition, Spinger Verlag, 1998.

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MATA KULIAH/

COURSE TITLE

SM 092303 ANALISIS FUNGSIONAL

SM 092303 FUNCTIONAL ANALYSIS

Credits: 3 sks / credits unit

Semester: 1

TUJUAN

PEMBELAJARAN/

Mahasiswa mampu menggunakan analisa secara matematis, menelaah suatu teorema serta menerapkannya pada masalah dalam bidang matematika dan bidang lainnya.

The students can do mathematical analysis, study and describe the thoerems and also aplly those thoerems in mathematical field and others

KOMPETENSI/

COMPETENCY

x Mahasiswa dapat menjelaskan sifat-sifat ruang vektor, ruang

metrik, ruang normsifat-sifat himpunan, dan sifat-sifat barisan pada ruang-ruang tersebut

x Mahasiswa dapat menjelaskan sifat-sifat ruang hasil kali dalam,

ortogonalitas vektor dan barisan ortonormal beserta penggunaanya

x Mahasiswa dapat menerapkan titik tetap Banach untuk

menyelesaikan masalah persamaan linear, persamaan diferensial dan persamaan integral dan teorema approksimasi pada ruang norm

Mahasiswa mengerti dan mampu menggunakan teorema spektral dan kaitannya dengan nilai eigen.

The students can explain the properties of vector space, metric space, norm space, set and the properties of sequences in those spaces.

The studens can explain the properties of inner product, orthogonality of vector, ortonomality of sequences.

The students can apply the Banach fixed point to linear equation, differetial equation and integral equation and approximation theorem in norm space

The students can explain and apply the spectral theorem and its correlation with eigen vector.

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SUBJECTS konvergensi barisan, barisan Cauchy

x Ruang norm, ruang Banach, ruang norm dimensi hingga,

operator linear, operator terbatas

x Ruang hasil kali dalam, ruang Hilbert, ortogonal dan komplemen

ortogonal, himpunan dan barisan ortonormal

x Teorema Hahn-Banach, dan terapannya pada operator linear

terbatas

x Teorema titik tetap Banach dan terapannya pada persamaan

linear, persamaan diferensial, persamaan integral

x Teori Approksimasi pada ruang norm, ketunggalan aproksimasi,

aproksimasi seragam

x Teori spektral dari operatro linear pada ruang norm untuk

dimensi hingga dan operator linear terbatas.

x Vector space, metric space, open and closed set, convergence of sequences, Cauchy sequence

x Norm space, Banach space, finite dimensional of norm space, linear operator, bounded operator

x Inner product space, Hilbert space, ortogonal and complement ortogonal, ortonormal set and sequences

x Hanh-Banach theorem and its application in bounded linear operator

x Banach Fixed point theorem and its application to linear differential and integral equation

x Approximation theory in norm space, uniqueness, uniform approximation

x Spectral theory of linear operator in norm space, in finite dimension and bounded operator

PUSTAKA UTAMA/

REFERENCES

x KREYSZIG, E., INTRODUCTION FUNCTIONAL ANALYSIS WITH

APPLICATION, 1978, JOHN WILEY & SONS

x ZEIDLER, E., APPLIED FUNCTIONAL ANALYSIS, 1995, SPRINGER

VERLAG

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COURSE TITLE

_SIMULASI

(MATA KULIAH WAJIB)

SM 092305: MATHEMATICAL MODELING AND

SIMULATION

(COMPULSARY COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

I

TUJUAN

PEMBELAJARAN/

x Mata kuliah ini membahas tentang metode atau teknik untuk

mengkonstruksi model matematika dari fenomena yang akan dikaji menggunakan hukum-hukum yang mengendalikan fenomena tersebut

x This course describes either method or technique to construct mathematical model of a considered phenomenon using a governed law of the phenomenon.

KOMPETENSI/

COMPETENCY

x Mampu mengikuti perkembangan Matematika, Sains dan

Teknologi

x Able to follow development of Mathematics, science and technology

x Mampu mengembangkan Matematika dan Terapannya

x Able to develop Mathematics and its applications

x Mampu mengimplementasikan kerangka berfikir matematis

untuk merancang, menganalisis, dan mengevaluasi pemecahan masalah nyata

x Able to implement the framework of mathematically mind to design, analyze and evaluate real problem solving

POKOK BAHASAN/

SUBJECTS

x Konsep dasar pemodelan matematika

x Basic concept of mathematical modeling

x Pendekatan pembentukan model : eksplorasi data dan

konfirmasi data

x Structuring model approach: data exploratory dan data confirmatory

x Pemodelan matematika lanjut

x Advanced mathematical modeling

x Contoh-contoh pemodelan matematika lanjut

x Examples of Advanced mathematical modeling

PUSTAKA UTAMA/

REFERENCES

x Bellomo, N. dan Preziosi, L., Modelling Mathematical Methods

and Scientific Computing, Italy: CRC Press, 1995

x Beltrami, E., Mathematical for Dynamic Modelling, New York,

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x Law, A.M. dan Kelton, W.D., Simulation Modelling and Analysis,

New York, USA: Mc Graw Hill,1990

x Johansson, R., System Modelling and Identification, New York,

USA: Prentice Hall International, 1993.

MATA KULIAH/

COURSE TITLE

SM 092307: BIOINFORMATIKA

(MATA KULIAH WAJIB)

SM 092307: BIOINFORMATICS

(COMPULSARY COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

I

TUJUAN

PEMBELAJARAN/

x Mata kuliah ini membahas tentang metode matematika dan

software tools yang digunakan untuk memodelkan, mensimulasikan dan memprediksi fungsi DNA.

x This course discuss about mathematical method and software tools which used for modeling, simulate, and prediction of DNA function.

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x Metode Matematika untuk pemodelan DNA

x Mathematical methods for DNA modeling.

x Metode komputasi lunak untuk pemodelan DNA

x Soft computing for DNA modeling

x Konsep dasar biologi molekuler dan data bioinformatics

x Basic concept of biology molecular and data bioinformatics

x Pengenalan tools bioinformatics

x Introduction of bioinformatica tools

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x Sequence comparations

x Pemodelan dan analisis

x Modeling and analysis

PUSTAKA UTAMA/

REFERENCES

x Polanski, A and M. Kimmel, Bioinformatic, Springer Inc, 2007

x Shen, SN and JA TuZynski, Theory and Mathematical Methods

for Bioinformatics, Springer Inc, 2008

x Christianini N and MW. Hahn, Computational Genomics,

Cambridge University Press, 2006

MATA KULIAH/

COURSE TITLE

SM 092302: KOMPUTASI NUMERIK

(MATA KULIAH WAJIB)

SM 092302: NUMERICAL COMPUTATION

(COMPULSARY COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

II

TUJUAN

PEMBELAJARAN/

x Matakuliah komputasi numerik ini menjelaskan metode

penyelesaian numerik dari persamaan differensial biasa dan/atau parsial menggunakan metode beda hingga, elemen hingga dan volume hingga dengan bantuan komputer

x This course describes numerical solution method of both/either ordinary differential equation(ODE) and/or partial differential equation(PDE)using the methods of finite difference, finite element and finite volume with computer

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x Masalah Nilai awal dari PD Biasa

x Initial Value Problem of ODE

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x Boundary Value Problem of PDE

x Metode Beda Hingga untuk PD Biasa dan Parsial

x Finite Difference Method for both ODE and PDE

x Metode Elemen Hingga

x Finite Element Method

x Metode Volume Hingga dan Metode Elemen Batas

x Finite Volume Method and Boundary Element Method

PUSTAKA UTAMA/

REFERENCES

x Hunter, P., FEM/BEM, New Zealand: Dept. of Engineering

Sciences, Auckland University, 2007

x Mitchell, A.R & Griffith, D.F., The Finite Difference Method in

Partial Diffrential Equations, New York: A Wiley- Interscience Publication (John Wiley & Sons) , 1980

x Griffiths, D.V. dan Smith, I.A., Numerical Methods for Engineers,

London: Blackwell Scientific Publications, 1991

x Whye-Teong Ang, A Beginner's Course in Boundary Element

Methods, New York: 2007

MATA KULIAH/

COURSE TITLE

SM 092305: KOMPUTASI JARINGAN

SYARAF TIRUAN

(MATA KULIAH WAJIB)

SM 092305: COMPUTATION OF ARTIFICIAL

NEURAL NETWORKS

(COMPULSARY COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

II

TUJUAN

PEMBELAJARAN/

LEARNING

x Matakuliah komputasi jaringan syaraf tiruan menjelaskan

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OBJECTIVES komputer dan dipakai untuk menyelesaikan masalah-masalah

pengenalan pola, peramalan, klasifikasi, klustering dan optimasi. x This course describes the algorithms that used to model data

using computer. Student be able to translate the algorithms become computer program and used to solve the problems of pattern recognition, forecasting, classification, clustering and optimization

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x Pemdelan JST dari JSB

x Modeling ANN from BNN

x Review pemrograman computer

x Review computer programming

x Masalah klasifikasi sederhana menggunakan perceptron, hebb

dan adaline

x Simple classification problems using perceptron, heb, and adaline

x Metode pengenalan pola menggunakan Hebb, Associative

Memory, BAM, dan MLP

x Pattern recognition methods using Hebb, Associative Memory, BAM, and MLP

x Metode klasifikasi menggunakan MLP, RBF, jaringan recurrent,

dan LVQ,

x Classification methods usingMLP, RBF, Recurrent Network and LVQ

x Metode peramalan menggunakan MLP, RBF, dan Recurrent

Network

x Forecasting methods using MLP, RBF, and Recurrent Network

x Metode clustering menggunakan Kohonen SOM dan SVM

x Clustering methods using Kohonen SOM and SVM

x Metode Optimasi menggunakan Kohonen, dan Hopfield

x Optimization methods using Kohonen and Hopfield

PUSTAKA UTAMA/

REFERENCES

x Fausett,L, Fundamentals of Neural Networks,Prentice Hall, New

Jersey, USA, 1994.

x Hassoum, MH, Fundamental of Artificial Neural Networks, MIT,

1995.

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University Press, 1996

x Duda, RO, Hart, PE, Stork, DG, Pattern Classification, John Wiley

and Sons, 2001

x Stork, DG and E. Yom-Tov, Computer Manual in MATLAB to

Accompany Pattern Classification, Second Edition (Paperback), John Wiley and Sons, 2004

MATA KULIAH/

COURSE TITLE

SM 092202: OPTIMASI DINAMIS

(MATA KULIAH PILIHAN)

SM 092202: DYNAMICS OPTIMIZATION

(ASSORTED COURSE TITLE)

Credits: 3 sks / credits unit

Semester: II

TUJUAN

PEMBELAJARAN/

x

Memberikan pemahaman kepada mahasiswa tentang

optimisasi dan aplikasinya

x

To provide the student with an understanding of the

optimization and their applications

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x Pengantar desain

x Introduction to Design,

x Perumusan Masalah desain opt8imum x Optimum Design Problem Formulation, x Metode optimasi grafis

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x Konsep desain optimum x Optimum Design Concepts,

x Metode Numerik untuk desain optimum tak terkendala x Numerical Methods for Unconstrained Optimum Design, x Metode Numerik untuk desain optimum terkendala x Numerical Methods for Constrained Optimum Design PUSTAKA UTAMA/

REFERENCES

Arora, J.S. Introduction to Optimum Design, Elsevier Academics

Press, 2004.

Bryson, A.E., Dynamics Optimizatio, Wiley , 2000

MATA KULIAH/

COURSE TITLE

SM 092204: LOGISTIK DAN METODE

PERENCANAAN TRANSPORTASI

(MATA KULIAH PILIHAN)

SM 092204: LOGISTIC AND TRANSPORTATION

PLANNING METHODS

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

II

TUJUAN

PEMBELAJARAN/

x Kuliah ini mendiskusikan tentang penjadwalan proyek, penjadwalan job-shop, penjadwalan sistem asemble fleksibel, penjadwalan lot economis, perencanaan dan penjadwalan dalam transportasi.

x The course discuss about project scheduling, job shop

scheduling, scheduling of flexible assembly systems, economic lot scheduling, and planning and scheduling in supply chains. It covers four areas in services, namely, reservations and timetabling, tournament scheduling, planning and scheduling in transportation

KOMPETENSI/

COMPETENCY

Teknologi

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POKOK BAHASAN/

SUBJECTS

x Pengantar sistem logistic

x Introduction of logistics system

x Meramalkan kebutuhan logistic

x Forecasting logistics demand

x Merencanakan jaringan logistic

x Planning logistics networks

x Menyelesaikan masalah manajemen persediaan

x Solving inventory management problem

x Merancang dan mengoperasikan gudang

x Design and operating a warehouse

x Merancang dan mengatur angkutan transportasi jarak dekat dan

jauh

x Design and manage short/long haul transportation

PUSTAKA UTAMA/

REFERENCES

x Ghiani, G, Laporte, G and R. Musmanno, An Introduction to

Logistics Systems Planning and Control, John Wiley and Sons,

Ltd, 2004

x Pinedo, ML, Planning and Scheduling in Manufacturing and Services, Springer Science, 2005

MATA KULIAH/

COURSE TITLE

SM 092206 TEORI DAN APLIKASI GRAF

(MATA KULIAH PILIHAN)

SM 092206 GRAPH THEORY AND APPLICATIONS

(MATA KULIAH PILIHAN)

Credits: 3 SKS / 3 Credit units

Semester:

II

TUJUAN

PEMBELAJARAN/

Agar memahami graph sebagai salah satu model matematika yang sangat penting untuk berbagai masalah.

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KOMPETENSI/

COMPETENCY

POKOK BAHASAN/

SUBJECTS

Pendahuluan (Pengertian Graph, beberapa jenis graph, graph pohon (pohon minimum), masalah lintasan terpendek, Graph planar (pengertian graph planar dan graph bidang), graph Euler (pengertian graph Euler dan semi Euler), graph Hamilton, pewarnaan graph (pewarnaan titik, pewarnaan sisi), masalah perjodohan, graph bipartite, graph berarah (turnamen, alur lalu lintas, network).

Introduction, graph tree, shortest distance problem, planar graph, Euler graph, Hamilton graph, Colouring graph, matching problem, bipartite graph, directed graph.

PUSTAKA UTAMA/

REFERENCES

x F. Hanary, ”Graph Theory”, Addison-Wesley Publishing Co

Inc., Massachussets USA, 1969

x Deo Narscyh, “Graph Theory with Applications to

Engineering and computer science Preslitice Hall Inc., Englewod Cliffs, N.J., USA

x I Ketut Budayasa, “Teori Graph and Aplikasinya”, Unesa

University Press, 2007

MATA KULIAH/

COURSE TITLE

SM 092208: DISPERSI ATMOSFIR

(MATA KULIAH PILIHAN)

SM 092208: ATMOSPHERIC DISPERSION

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

II

TUJUAN

PEMBELAJARAN/

x Memberikan wawasan tentang teori dispersi atmosfir dan menjelaskan tentang prinsip-prinsip dasar tentang pemodelan dispersi atmosfir

x To give an introduction to the theory of atmospheric dispersion and to describe the basic principles of atmospheric dispersion modelling

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COMPETENCY _x Able to follow development of Mathematics, science and

technology

POKOK BAHASAN/

SUBJECTS

x Pengangkutan skalar pada Atmosfir x Scalar Transport in the Atmosphere x Proses-proses pengangkutan x Transport Processes

x Lapisan batas atmosfir

x The Atmospheric Boundary Layer

x Sumber-sumber titik penghasil polutan yang kontinyu x Continuous Point Sources of Pollutant

x Dispersi pada lingkungan nyata x Dispersion in Real Environments

x Kepulan Asap Gauss dari cerobong yang tinggi x Gaussian Plumes from High Chimneys x Deposisi

x Deposition

x Tipe-tipe dari model dispersi atmosfir x Types of Atmospheric Dispersion Models

x Reaksi-reaksi kimiawi dari polutan yang ada di atmosfir x Chemical Reaction of Atmospheric Pollutants

x Pembaganan pada Penyelesaian Numerik x Numerical Schemes

PUSTAKA UTAMA/

REFERENCES

x Barrat, R., Atmospheric Dispersion Modelling, 1st Edition,

Earthscan Publications, 2001

x Colls, J., Air Pollution, 1st Edition, Spon Press (UK), 2002

x European Process Safety Centre, Atmospheric Dispersion, 1st

Edition, Rugby: Institution of Chemical Engineers, 1999

x Schnelle, K.B. and Dey, P.R., Atmospheric Dispersion Modeling

Compliance Guide, 1st Edition, McGraw-Hill Professional, 1999

x Turner, D.B., Workbook of Atmospheric Dispersion Estimates: An

Introduction to Dispersion Modeling, 2nd Edition, CRC Press, 1994

x Zannetti, P., Air pollution modeling : theories, computational

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MATA KULIAH/

COURSE TITLE

SM 092210: KECERDASAN BUATAN

(MATA KULIAH PILIHAN)

SM 092210: ARTIFICIAL INTELLIGENCE

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

III

TUJUAN

PEMBELAJARAN/

x Matakuliah kecerdasan buatan mendiskusikan metode merubah

komputer menjadi cerdas yang mampu bernalar sebaik manusia. Dalam kuliah ini mahasiswa dituntut untuk bisa mengimplementasikan beberapa metode agar komputer bisa menjadi cerdas dan bisa menyelesaikan suatu masalah yang membutuhkan kecerdasan dalam menyelesaikanya.

x Artificial Intelligence course discuss the methods to change the computer become intelligence able to reasoning as well as human. In this course student should implemented some methods in order give intelligence to the computer and able to solve a problem that need intelligence.

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x konsep kecerdasan buatan,

x concept of artificial intelligence

x teknik penyelesaian masalah menggunakan kecerdasan buatan

x problem-solver technique using artificial intelligence

x teknik pencarian, representasi pengetahuan, ketidakpastian

x searching technique, knowledge representation, uncertainty

x sistem pakar, and sistem pakar fuzzy

x expert system and fuzzy expert system

x algoritma genetika dan pemrograman genetika

x genetics algorithms and genetic programming

x particle swarm optimization dan algoritma koloni semut

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PUSTAKA UTAMA/

REFERENCES

x Stuart J. Russel and Peter Norvig, Artificial Intelligence A

Modern Approach, McGrawHill, 2003

x Eleane Rich and Kevin Knight, Artificial Intelligence, McGrawHill, 2000

x John Durkin, Expert Systems: design and development, Prentice Hall, 2003

MATA KULIAH/

COURSE TITLE

SM 092212: MATEMATIKA SISTEM (MATA KULIAH PILIHAN) SM 092212: MATEMATICAL SYSTEM (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units

Semester: II

TUJUAN

PEMBELAJARAN/

x Mahasiswa mengerti secara umum matematika sistem dan notasi yang berhubungan, teori ruang keadaan, keterkontrolan dan stabilitas

x The Students understand to the generalize of matematical system and relate notion, the State Space Theory, controlability and the Stability

KOMPETENSI/

COMPETENCY

x Mahasiswa bisa menggunakan hukum konservasi, prinsip-prinsip fenomena dan fisika untuk membuat model matematika dari sistem

x The Students can use conservation laws,

phenomenological and physical principles to make mathematical models of systems

x Mahasiswa mampu melinierisasi dari sistem nonlinear dan menyelesaikan sistem differensial linier

x The Students able to linearize of non linear system and solve linear differential systems.

x Mahasiswa mampu menganalisis keterkontrolan dan keteramatan dari sistem

x The students able to analyze the controllability and observability of systems

x Mahasiswa mampu menganalisa perilaku input-output dari sistem

x The students able to analyze the Input Output Behaviour of the systems

x Mahasiswa mampu menerapkan keterkontrolan sistem untuk menstabilkan sistem

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x Mahasiswa mampu menetapkan kriteria kestabilan dari sistem

x The students able to determine the stability criteria of the systems

POKOK BAHASAN/

SUBJECTS

x Model-model matematika x Mathematical Models

x Pengantar teori ruang keadaan x Introduction to State Space Theory x Teori stabilitas

x Stability Theory

PUSTAKA UTAMA/

REFERENCES

x Subiono, Matematika Sistem, Versi 2.0, buku ajar Jurusan Matematika FMIPA-ITS, 2010.

x Olsder G.j. and J.W. van der Woude, “Mathematical Systems Theory”, Delft Uitgavers Maatschappij, 1994. x Hinrichsen D. and T. Pritchard “ Mathematical Systems

Theory I Modelling, State Space Analysis, Stability and Robustness”, Springer Verlag ,2004

MATA KULIAH/

COURSE TITLE

SM 092214 ASIMILASI DATA

SM 092214 DATA ASSIMILATION

Credits: 3 sks / credits unit

Mahasiswa mengerti dan mampu menerapkan berbagai algoritma dalam asimilasi data pada masalah identifikasi parameter dan estimasi variable keadaan dari system dinamik stokastik.

The students understand and can apply the algorithms of data assimilation to identify parameters and estimate the state variable of dynamical stochastic system.

KOMPETENSI/

COMPETENCY

x Mahasiswa mengerti metode asimilasi data dan model-model

sistem dimana metode asimilasi data dapat digunakan.

x Mahasiswa mampu menjelaskan beberapa metode estimasi dan

perkembangan metode asimilasi data.

x Mahasiswa dapat menerapkan asimilasi data pada model dinamik

stokastik dan deterministik

x Mahasiswa mampu menjelaskan dan menerapkan berbagai

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x The students understand about data assimilation method and

where it’s can be applied.

x The students can explain several estimation methods and the

pathways into data assimilation

x The students can apply data assimilation to dynamical

stochastic/deterministic model

x The students can explain and apply the developing of Kalman filter

as data assimilation method.

POKOK BAHASAN/

SUBJECTS

x Pengertian metode asimilasi data: peramalan, model, keteramatan, analisa sensitivitas, predictable.

x Model-model yang digunakan dalam asimilasi data

x Beberapa metode asimilasi data: Model statis stokastik, model dinamik deterministic, model dinamik stokastik

x Beberapa perkembangan algoritma Kalman Filter: Extended Kalman Filter, RRSQRT filter, Ensemble Kalman Filter, Hibrid

filter

x Studi kasus penerapan asimilasi data

x Data assimilation: forecasting, modeling, observations, sensitivity analysis

x Modeling in data assimilation

x Some of data assimilation methods: stochastic static model, deterministic dynamic model, stochastic dynamic model

x The advantage of Kalman filter: extended Kalman filter, RRSQRT filter, Ensemble Kalman Filter, Hibrid filter

x Case studies

PUSTAKA UTAMA/

REFERENCES

x LEWIS, J.M., LAKSHMIVARAHAN, DHALL, S.K., 2006, DYNAMIC

DATA ASSIMILATION: A LEAST SQUARES APPROACH, CAMBRIDE

x KALNAY, 2003, ATMOSPHERIC MODELING, DATA

ASSIMILATION AND PREDICTABILITY, CAMBRIDGE

MATA KULIAH/

COURSE TITLE

SM 092201: ALJABAR MAX PLUS (MATA KULIAH PILIHAN) SM 092201: MAX PLUS ALGEBRA (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units

Semester: III

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OBJECTIVES x The Students understand to the generalize of max-plus algebra and related notion, the spectral theory, periodic and asymphotic qualitative behavior and the cycle time vector.

KOMPETENSI/

COMPETENCY

x Mahasiswa mampu menerapkan aljabar maxplus di masalah nyata

x The Students be able to apply max-plus algebra in the real problems

x Mahasiswa mampu mampu mendapatkan nilai eigen dan vektor eigen dari matriks-matriks irreducible dan reducible x The students able to find eigenvalues and eigenvectors of

irreducible an reducible matrices.

x Mahasiswa mampu menganalisis perilaku periodik dari model linier max-plus

x The students able to analyze the periodic behavior of the max plus linear model.

POKOK BAHASAN/

SUBJECTS

x Aljabar Max-Plus x Max-Plus Algebra x Teori Spektral x Spectral Theory

x Perilaku periodik dan vektor siklus waktu x Periodic behavior and the cycle-time vector x Perilaku kualitatif asimtotik

x Asympotic Qualitative Behavior

x Prosedur numerik dari nilai eigen matriks irreducible dan reducible

x Numerical Procedure of eigenvalues of irreducible and reducible matrices

x Introduction to Petri Nets

PUSTAKA UTAMA/

REFERENCES

x Subiono, Aljabar Max-Plus, buku ajar Jurusan Matematika FMIPA-ITS, 2010.

x Olsder G.j., Heidegott B. and J.W. van der woude, Maxplus at Work, Modelling and Analysis of Synchronized System : A Course on Max-Plus Algebra and ITS Applications, Princeton University Press, 2006

x Subiono, andJ.W. van Wounde, “Power Algorithms for (mas,+) – and Bipartite(Min,max,+) - Systems”, Discreate Event Dynamic System : Theory and Applications, Volume 10, pp 369-389, 2002

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MATA KULIAH/

COURSE TITLE

SM 092203: KOMPUTASI DINAMIKA FLUIDA

(MATA KULIAH PILIHAN)

SM 092203: COMPUTATIONAL FLUID DYNAMICS

(CFD)

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

III

TUJUAN

PEMBELAJARAN/

x Matakuliah komputasi dinamika fluida ini membahas tentang

penggunaan komputer dan teknik numerik untuk menyelesaikan permasalahan yang berkaitan dengan aliran fluida

x The computational fluid dynamics course describes the use of computers and numerical techniques to solve problems involving fluid flow

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x Persamaan aliran fluida

x Fluid flow equation

x Persamaan Pengangkutan Skalar

x Scalar transport equation

x Persamaan momentum

x Momentum equation

x Turbulen

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x Model Turbulen dalam KDF

x Turbulence modeling on the CFD

x Proses Komputasi Dinamika Fluida

x The Computational Fluid Dynamics Process

PUSTAKA UTAMA/

REFERENCES

x Anderson, J. D. Jr., Computational Fluid Dynamics (The Basics

with Applications), International Edition, New York, USA: Mc Graw-Hill, 1995

x Hoffmann, K. A. and Chiang, S. T., Computational Fluid Dynamics

For Engineers, Wichita, USA: Engineering Education System, 1995

x Chung, T.J., Computational Fluid Dynamics, Cambridge: Cambridge University Press, 2002

x Welty, J.R., et al., Fundamentals of Momentum, Heat and Mass

Transfer, 3rd Edition, New York, USA: John Wiley & Sons, Inc.,

1995

x Versteeg, H.K. and Malalasekera, W., An Introduction to Computational Fluid Dynamics – The Finite Volume Method, Second Edition, England: Prentice Hall - Pearson Education Ltd., 2007.

x Tu, J.Y., Yeoh, G.H. and Liu, G.Q., Computational Fluid

Dynamics-A Practical Dynamics-Approach, Oxford, UK: Butterworth-Heinemann

Publications, 2008

x Yeoh, G.H. and Yuen, K.K., Computational Fluid Dynamics in Fire Engineering, Oxford, UK: Butterworth-Heinemann Publications, 2009

MATA KULIAH/

COURSE TITLE

SM 092205: KONTROL OPTIMUM

(MATA KULIAH PILIHAN)

SM 092205: OPTIMAL CONTROL

(ASSORTED COURSE TITLE)

Credits: 3 sks / credits unit

Semester: 3

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control optimal, pemodelan, aplikasi, simulasi dan komputasi

x To provide the student with an understanding of the optimal control problem, modelling, application, simulation and computation.

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x

Review kalkulus variasi

x

Review calculus of variation,

x

Kontrol optimal: system waktu diskrit dan system waktu

kontinyu

x

optimal control: Discrete-time systems and

continuous-time systems,

x

Kontrol optimal terkendala dan tak terkendala

x

unconstrained and constrained optimal control,

x

waktu akhir tetap dan bebas

x

fixed and free final time,

x

Aplikasi dan simulasi

x

application and simulation,

x

metode langung dan tak langsung

x

direct and indirect method,

x

Komputasi control optimal

x

computational optimal control

.

PUSTAKA UTAMA/

REFERENCES

1. Subchan, S and Zbikowski, R., Computational Optimal

Control: Tools and Practice, Wiley, 2009.

2. Lewis, F. dan Syrmos Vassilis, Optimal Control, John

Wiley & Sons, Singapore, 1995.

x

Kamien, ML and Schwartz, N.L.,

Dynamic Optimizatio

,

North-Holland, Amsterdam, 1993.

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MATA KULIAH/

COURSE TITLE

SM 092207: KAPSEL PEMODELAN DAN

SIMULASI

(MATA KULIAH PILIHAN)

SM 092207: SELECTED TOPICS OF

MODELING AND SIMULATION

(ASSORTED COURSE TITLE)

Credits: 3 sks / credits unit

Semester: III

TUJUAN

PEMBELAJARAN/

x Menyiapkan mahasiswa pemahaman topic-topik saat ini tentang

pemodelan dan simulasi

x To provide the student with an understanding of the current research topic in modelling and simulation

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x Tergantung kepada dosen pengampu, akan diinformasikan

kepada mahasiswa sebelum masa perkuliahan

Depend on the lecture, it will be informed to the student before semester begin

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MATA KULIAH/

COURSE TITLE

SM 092303 ANALISIS FUNGSIONAL

SM 092303 FUNCTIONAL ANALYSIS

Kredit: 3 sks

Credits:

3 credits unit

Semester: I

TUJUAN

PEMBELAJARAN/

Diharapkan mahasiswa mendapat pengetahuan dan pemahaman tentang pokok-pokok analisis fungsional, khususnya tentang ruang Banach, ruang Hilbert, dan operator linear kompak, serta mengenal plikasinya.

After completing this course, the students should have knowledge and comprehension of fundamental concept of functional analysis, especially about Banach spaces, Hilbert spaces, and compact linear operators, and be acquainted to their applications.

KOMPETENSI/

COMPETENCY

x Dapat mengenali ruang Banach dan ruang Hilbert, berserta

sifat-sifat utamanya.

x Dapat menunjukkan sifat-sifat operator linear terbatas, operator

kompak, dan dapat membuktikan sifat-sifat utama operator kompak.

x Dapat membuktikan kelengkapan ruang Lp, dan mengenal

penerapnnya.

x Able to identify Banach spaces and Hilbert spaces, and address their main properties.

x Able to show the main properties of bounded linear operators and compact operators, and prove the fundamental properties of compact operators.

x Able to prove the completeness of the Lp spaces, and understand their applications.

POKOK BAHASAN/

SUBJECTS

x Ruang Banach dan ruang Hilbert: pelengkapan, operator terbatas,

jumlahan langsung, basis ortonormal, jumlahan ortogonal.

x Operator-operator kompak: definisi dan sifat-sifat pokok, teorema

spektral untuk operator simetrik kompak.

x Integrasi Lebesgue: fungsi terukur, integral Lebesgue, pengertian

“hampir dimana-mana”, ruang Lebesgue Lp, kelengkapan ruang Lp.

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x Banach and Hilbert spaces: completion, bounded operators, direct sum, orthonormal basis, orthogonal sum.

x Compact operators: definition and basic properties, spectral theorem for compact symmetric operators.

x Lebesgue integration: measurable functions, Lebesgue integral, the terminology of “almost everywhere”, Lebesgue space Lp, completeness of Lp.

x The dual of Lp: decomposition of measure, complex measure, the dual of Lp.

PUSTAKA UTAMA/

REFERENCES

x Zeidler, E., “Applied Functional Analysis, Application to

Mathematical Physics”, Springer-Verlag, New York, 1995.

Conway, J. B., “A Course in Functional Analysis”, Graudate Text

in Mathematics, 96, Springer-Verlag, New York, 1990.

MATA KULIAH/

COURSE TITLE

SM 092211: KAPSEL ANALISIS TERAPAN

(MATA KULIAH PILIHAN)

SM 092211: SELECTED TOPICS OF

APPLIED ANALYSIS

(ASSORTED COURSE TITLE)

Credits: 3 sks / credits unit

Semester: III

TUJUAN

PEMBELAJARAN/

x

Menyiapkan mahasiswa pemahaman topic-topik saat ini

tentang pemodelan dan simulasi

x

To provide the student with an understanding of the

current research topic in modelling and simulation

KOMPETENSI/

COMPETENCY

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POKOK BAHASAN/

SUBJECTS

x Tergantung kepada dosen pengampu, akan diinformasikan

kepada mahasiswa sebelum masa perkuliahan

Depend on the lecture, it will be informed to the student before semester begin

PUSTAKA UTAMA/

REFERENCES

MATA KULIAH/

COURSE TITLE

SM 092213: MULTI-KRITERIA OPTIMUM

(MATA KULIAH PILIHAN)

SM 092307: MULTICRITERIA OPTIMIZATION

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

I

TUJUAN

PEMBELAJARAN/

x Mahasiswa mampu membuat model keputusan dalam

menyelesaikan masalah yang berkarakteristik multicriteria secara optimal

x Student able to model decision making to solve problem which

have optimal multicriteria characteristic

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

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x Teknik skalarisasi x Metode non skalarisasi x Multikriteriapemrograman linier x Metode multi objektif simplex x Multiobjektive criteria optimisasi PUSTAKA UTAMA/

REFERENCES

x Matthias Ehrgott, Multicriteria Optimization, Springer Verlang Berlin, 2005

x Statnikov R.B., Multicriteria Design: Optimization and Identification, Kluwer Academic Publisher, 1999

MATA KULIAH/

COURSE TITLE

SM 092215: ANALISIS TIME SERIES

(MATA KULIAH PILIHAN)

SM 092215: TIME SERIES ANALYSIS

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

III

TUJUAN

PEMBELAJARAN/

x Kuliah ini mendiskusikan karakteristik dari time-series,

dasar-dasar regresi, teknik untuk data time series, pemodelan univariate ARIMA, proses GARCH, dan multivariate ARMAX. x The course discusses the characteristics of time series, a

background in regression , techniques for time series data, univariate ARIMA modeling, GARCH processes, and multivariate ARMAX models.

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x Karakteristik dari time series

x characteristics of time series

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x introducing the fundamental concepts of time plot models

x Latar belakang dalam regresi

x background in regression

x teknik-teknik untuk data time-series

x techniques for time series data dan nonstatsioner

x pemodelan univariate ARIMA

x univariate ARIMA modeling

x proses-proses GARCH, model threshold, regresi dengan

error-eror autokorelasi, regresi tundaan, pemodelan fungsi alih x GARCH processes, threshold models, regression with

autocorrelated errors, lagged regression, transfer function modeling

x Model-model multivariate ARMAX

x multivariate ARMAX models.

PUSTAKA UTAMA/

REFERENCES

x Kirchgässner G and J. Wolters, Introduction to Modern Time

Series Analysis, Springer-Verlag, Berlin, 2007

x Brockwell, PJ and RA. Davis, Introduction to Time Series and Forecasting, Springer-Verlag New York, Inc McGrawHill, 2002

x Shumway RH and DS Stoffer. Time Series Analysis and Its Applications, Springer Science+Business Media, LLC, 2006

MATA KULIAH/

COURSE TITLE

SM 092217: TEORI RESIKO DAN ANALISIS

KEPUTUSAN

(MATA KULIAH PILIHAN)

SM 092217: RISK THEORY AND DECISION ANALYSIS

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

I

TUJUAN

PEMBELAJARAN/

x Mahasiswa mampu menerapkan matematika dalam

menganalisis resiko dalam setiap pengambilan keputusan.

x Student able to apply mathematics to risk analysis on decision

making

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COMPETENCY Teknologi

POKOK BAHASAN/

SUBJECTS

x Resiko dan analisis keputusan x Risk and decision analysis x Proses analisis keputusan x Decision analysis process x Kebijakan keputusan x Decision policy

x Utilitas dan keputusan multi kriteria x Utility and multicriteria decision x Pohon keputusan

x Decision tree x Penetapan dan bias x Judgment and bias x Menghubungkan resiko x Relating risk

x Stochastics variance PUSTAKA UTAMA/

REFERENCES

x Chavas J.P, Risk Analysis in Theory and Practice, Elsevier Inc, 2004

x John Schuyler, Risk and Decision Analysis in Projects, Project

Managemet Institute, Pennsylvania USA, 2001

MATA KULIAH/

COURSE TITLE

SM 092219: SISTEM FUZZY

(MATA KULIAH PILIHAN)

SM 092219: FUZZY SYSTEM

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

III

TUJUAN

PEMBELAJARAN/

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Kurikulum/

keputusan fuzzy, dan forecasting-clustering fuzzy. x To give knowledges about why fuzzy system, operation on

fuzzy system, fuzzy relationship, fuzzy logic, fuzzy decision making, and fuzzy clustering/forecasting.

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x Kenapa sistem fuzzy?

x Why fuzzy system?

x Matematika Himpunan Crsip vs Fuzzy

x Mathematics Crisp vs Fuzzy Set

x Fungsi keanggotaan

x Membership function

x Operasi-operasi pada himpunan fuzzy

x Operation on Fuzzy Set

x Variabellinguistic

x Linguistic Variables

x Relasi fuzzy, dan Logika Fuzzy

x Fuzzy relation and fuzzy logic

x Model-model pengambilan keputusan fuzzy

x Models of fuzzy decision making

x Forecasting dan clustering fuzzy

x Fuzzy forcasting and clustering

PUSTAKA UTAMA/

REFERENCES

x Buckley J, and E. Eslami,An Introduction to Fuzzy Logic and

Fuzzy Sets, Physica Heidelberg, 2001,

x Klir, GJ and B. Juan, Fuzzy Set and Fuzzy Logic, Prentice Hall, New

Jersey, 2001

x Zimmerman H.J, Fuzzy Set Theory and Its Applications, Kluwer

Academic Publisher, 1996.

x Zadeh, LA., Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected

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MATA KULIAH/

COURSE TITLE

SM 092221: PENGOLAHAN CITRA

(MATA KULIAH PILIHAN)

SM 092221: IMAGE PROCESSING

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

I

TUJUAN

PEMBELAJARAN/

x Mahasiswa mampu memahami konsep dasar dari pengolangan

citra digital dan menerapkannya ke aplikasi yang lebih kompleks

x Students are able to comprehend basic concepts of digital image processing and apply it to more complex application.

KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x Konsep dasar dari pemrosesan citra

x The basic steps of image processing

x Elemen system DIP, model citra sederhana, kuantisasi dan

sampling

x DIP system element, simple Image Model, quantization and sampling,

x Transformasi Fourier, transformasi Fourier Diskrit 2D

x Fourier transformation, 2D Discrete Fourier Transforms

x Manipulasi citra: model warna, manipulasi RGB, metode

frekuensi dan spasial

x Image Manipulation: Color model, RGB manipulation, Frequency and spatial method,

x Transformasi geometri

x Geometry Transforms,

x Perbaikan citra

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x Segmentasi citra

x Image Segmentation,

x Pengantar pola

x Introduction to pattern,

x Kompresi citra

x Image compression.

PUSTAKA UTAMA/

REFERENCES

x Go Rafael C. Gonzalez and Richard E. Woods, Digital Image

Processing, Addison Wesley. 1993

x Robert J. Schalkoff, Digital Image Processing and Computer

Vision, John Wiley and Son. 1999

Anil K. Jain, Fundamental of Digital Image Processing, Prentice Hall, 1989

MATA KULIAH/

COURSE TITLE

SM 092209: ANALISIS DATA SURVIVAL

(MATA KULIAH PILIHAN)

SM 092209: SURVIVAL DATA ANALYSIS

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

I

TUJUAN

PEMBELAJARAN/

x Mahasiswa mampu menganalisis data daya survive dengan beberapa pendekatan model

x Students are able to analyze survival data with some model approach

KOMPETENSI/

COMPETENCY

Teknologi

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POKOK BAHASAN/

SUBJECTS

x Pengantar analisis survival x Introduction to Survival Analysis

x Kurva survival Kaplan-Meier dan Uji log rank

x Kaplan–Meier Survival Curves and the Log–Rank Test . x Model bencana proporsional Cox dan karakteristiknya

x The Cox Proportional Hazards Model and Its

Characteristics

x Mengevaluasi bencana proporsional x Evaluating the Proportional Hazards x Prosedur berjenjang Cox

x The Stratified Cox Procedure

x Perluasan daribnecana proporsional Cox x Extension of the Cox Proportional Hazards x Model-model Survival Parametrik

x Parametric Survival Models x Analisis Survival Kejadian berulang x Recurrent Event Survival Analysis x Komptensi Analisis resiko survival x Competing Risks Survival Analysis

PUSTAKA UTAMA/

REFERENCES

x Kleinbaum DG and M. Klein, Survival Analysis, Springer Science+Business Media, Inc., 2005

x Cox, D.R. and Oakes, D., Analysis of Survival Data, Chapman&Hall, 1994,

x Collect,D., Modelling Survival Data in Medical Research, Chapman & Hall. 1996,

MATA KULIAH/

COURSE TITLE

SM 092225: OPTIMASI HEURISTIK

(MATA KULIAH PILIHAN)

SM 092225: HEURISTICS OPTIMIZATION

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

I

TUJUAN

PEMBELAJARAN/

x Mahasiswa mampu memahami metode-metode heuristik dan

mengimplementasikannya untuk menyelesaikan masalah optimasi

x Student are able to comprehend heuristics methods and implement it to solve optimization problem

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COMPETENCY _x Able to follow development of Mathematics, science and

technology

POKOK BAHASAN/

SUBJECTS

x Simulated Annealling x Scatter Search x Tabu Search

x Evolutionary Algorithms

x Genetics Algorithms and Genetics Programming x Memetics Algorithms

x Ant Colony Algorithms x Simulated Annealling

PUSTAKA UTAMA/

REFERENCES

x Petrowski J.D. and P.S.E. Taillard, Metaheuristics for Hard Optimization, Springer-Verlag Berlin Heidelberg, 2006 x Glover F. and Kochenberger G.A., Hand Book of

Metaheuristics, Kluwer Academic Publishers, 2003

x Doerner K.F., Gendreau M., Greistorfer P., Gutjahr W.J, Hartl RF. and M. Reimann KF , Metaheuristics Progress in Complex Systems Optimization, Springer Science + Business Media, LLC 2007

MATA KULIAH/

COURSE TITLE

SM 092227: OPTIMASI KOMBINATORIAL

(MATA KULIAH PILIHAN)

SM 092227: COMBINATORIC OPTIMIZATION

(ASSORTED COURSE TITLE)

Credits: 3 SKS / 3 Credit units

Semester:

I

TUJUAN

PEMBELAJARAN/

x Memberikan pengetahuan kepada mahasiswa prinsip

matematika untuk memodelkan dan mengembangkan penyelesaian optimal permasalahan combinatorial

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KOMPETENSI/

COMPETENCY

Teknologi

POKOK BAHASAN/

SUBJECTS

x Polytopes and Linear Programming x Matroids and Greedy Algorithm x Minimum-Weights Dipaths x Matroids Intersection x Matching

x Networks Flow and Cuts

x Cutting Planes for Integer Programming x Branch and Bound for discrete optimization x Optimizing Submodular Function

PUSTAKA UTAMA/

REFERENCES

x Jon Lee, A First Course in Combinatorial Optimization, Cambride Text in Applied Mathematics - Cambride University Press, 2004