[FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM]...

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[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

� AKADEMISI DI BIDANG MATEMATIKA DAN TERAPANNYA � PENELITI DI BIDANG MATEMATIKA DAN TERAPANNYA

Graduate Competence

� ACADEMICIAN IN MATHEMATICS AND ITS APPLICATIONS � 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

3

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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

Jumlah sks/Total of credits 42

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DEPARTMENT OF MATHEMATICS PROGRAM PASCASARJANA/MAGISTER PROGRAM SILABUS KURIKULUM/COURSE SYLLABUS

MATA KULIAH/ COURSE TITLE

SM 092301: ALJABAR (MATA KULIAH WAJIB) SM 092301: ALGEBRA (COMPULSARY COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: I

TUJUAN PEMBELAJARAN/ LEARNING OBJECTIVES

� Mahasiswa mampu memahami secara umum struktur aljabar dan notasinya.

� The Students will be Understand to the generalize of the

structures algebra and related notion.

KOMPETENSI/ COMPETENCY

� Mahasiswa mampu menerapkan aljabar dalam matematika dan masalah riil

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

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

POKOK BAHASAN/ SUBJECTS

� Grup dan semigrup � Grup and Semigrup � Field berhingga dan Polinomial � 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.

� Subiono, Aljabar, buku ajar Matematika FMIPA ITS, 2009

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SM 092303 ANALISIS FUNGSIONAL SM 092303 FUNCTIONAL ANALYSIS Credits: 3 sks / credits unit Semester: 1


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


� Mahasiswa dapat menjelaskan sifat-sifat ruang vektor, ruang

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

� Mahasiswa dapat menjelaskan sifat-sifat ruang hasil kali dalam, ortogonalitas vektor dan barisan ortonormal beserta penggunaanya

� 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.

POKOK BAHASAN/ � Ruang vector, ruang metrics, himpunan buka dan tutup,

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SUBJECTS konvergensi barisan, barisan Cauchy � Ruang norm, ruang Banach, ruang norm dimensi hingga,

operator linear, operator terbatas � Ruang hasil kali dalam, ruang Hilbert, ortogonal dan komplemen

ortogonal, himpunan dan barisan ortonormal � Teorema Hahn-Banach, dan terapannya pada operator linear

terbatas � Teorema titik tetap Banach dan terapannya pada persamaan

linear, persamaan diferensial, persamaan integral � Teori Approksimasi pada ruang norm, ketunggalan aproksimasi,

aproksimasi seragam � Teori spektral dari operatro linear pada ruang norm untuk

dimensi hingga dan operator linear terbatas. � Vector space, metric space, open and closed set, convergence of

sequences, Cauchy sequence � Norm space, Banach space, finite dimensional of norm space,

linear operator, bounded operator � Inner product space, Hilbert space, ortogonal and complement

ortogonal, ortonormal set and sequences � Hanh-Banach theorem and its application in bounded linear

operator � Banach Fixed point theorem and its application to linear

differential and integral equation � Approximation theory in norm space, uniqueness, uniform

approximation � Spectral theory of linear operator in norm space, in finite

dimension and bounded operator


� KREYSZIG, E., INTRODUCTION FUNCTIONAL ANALYSIS WITH APPLICATION, 1978, JOHN WILEY & SONS

� ZEIDLER, E., APPLIED FUNCTIONAL ANALYSIS, 1995, SPRINGER VERLAG

MATA KULIAH/ SM 092305: PEMODELAN MATEMATIKA DAN

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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


� Mata kuliah ini membahas tentang metode atau teknik untuk mengkonstruksi model matematika dari fenomena yang akan dikaji menggunakan hukum-hukum yang mengendalikan fenomena tersebut

� This course describes either method or technique to

construct mathematical model of a considered phenomenon using a governed law of the phenomenon.


� Mampu mengikuti perkembangan Matematika, Sains dan Teknologi

� Able to follow development of Mathematics, science and technology

� Mampu mengembangkan Matematika dan Terapannya � Able to develop Mathematics and its applications � Mampu mengimplementasikan kerangka berfikir matematis

untuk merancang, menganalisis, dan mengevaluasi pemecahan masalah nyata

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


� Konsep dasar pemodelan matematika � Basic concept of mathematical modeling � Pendekatan pembentukan model : eksplorasi data dan

konfirmasi data � Structuring model approach: data exploratory dan data

confirmatory � Pemodelan matematika lanjut � Advanced mathematical modeling � Contoh-contoh pemodelan matematika lanjut � Examples of Advanced mathematical modeling


� Bellomo, N. dan Preziosi, L., Modelling Mathematical Methods and Scientific Computing, Italy: CRC Press, 1995

� Beltrami, E., Mathematical for Dynamic Modelling, New York, USA: Academic Press,1987

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� Law, A.M. dan Kelton, W.D., Simulation Modelling and Analysis, New York, USA: Mc Graw Hill,1990

� Johansson, R., System Modelling and Identification, New York, USA: Prentice Hall International, 1993.


SM 092307: BIOINFORMATIKA (MATA KULIAH WAJIB) SM 092307: BIOINFORMATICS (COMPULSARY COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: I


� Mata kuliah ini membahas tentang metode matematika dan software tools yang digunakan untuk memodelkan, mensimulasikan dan memprediksi fungsi DNA.

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








� Metode Matematika untuk pemodelan DNA � Mathematical methods for DNA modeling. � Metode komputasi lunak untuk pemodelan DNA � Soft computing for DNA modeling � Konsep dasar biologi molekuler dan data bioinformatics � Basic concept of biology molecular and data bioinformatics � Pengenalan tools bioinformatics � Introduction of bioinformatica tools � Komparasi sequence

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� Sequence comparations � Pemodelan dan analisis � Modeling and analysis


� Polanski, A and M. Kimmel, Bioinformatic, Springer Inc, 2007 � Shen, SN and JA TuZynski, Theory and Mathematical Methods

for Bioinformatics, Springer Inc, 2008 � Christianini N and MW. Hahn, Computational Genomics,

Cambridge University Press, 2006


SM 092302: KOMPUTASI NUMERIK (MATA KULIAH WAJIB) SM 092302: NUMERICAL COMPUTATION (COMPULSARY COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: II


� 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

� 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








� Masalah Nilai awal dari PD Biasa � Initial Value Problem of ODE � Masalah Nilai Batas dari PD Parsial

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� Boundary Value Problem of PDE � Metode Beda Hingga untuk PD Biasa dan Parsial � Finite Difference Method for both ODE and PDE � Metode Elemen Hingga � Finite Element Method � Metode Volume Hingga dan Metode Elemen Batas � Finite Volume Method and Boundary Element Method


� Hunter, P., FEM/BEM, New Zealand: Dept. of Engineering Sciences, Auckland University, 2007

� Mitchell, A.R & Griffith, D.F., The Finite Difference Method in Partial Diffrential Equations, New York: A Wiley- Interscience Publication (John Wiley & Sons) , 1980

� Griffiths, D.V. dan Smith, I.A., Numerical Methods for Engineers, London: Blackwell Scientific Publications, 1991

� Whye-Teong Ang, A Beginner's Course in Boundary Element Methods, New York: 2007


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

� Matakuliah komputasi jaringan syaraf tiruan menjelaskan algoritma-algoritma yang dipakai untuk memodelkan data dengan bantuan komputer. Mahasiswa mampu menterjemahkan langsung algoritma menjadi program

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OBJECTIVES komputer dan dipakai untuk menyelesaikan masalah-masalah pengenalan pola, peramalan, klasifikasi, klustering dan optimasi.

� 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








� Pemdelan JST dari JSB � Modeling ANN from BNN � Review pemrograman computer � Review computer programming � Masalah klasifikasi sederhana menggunakan perceptron, hebb

dan adaline � Simple classification problems using perceptron, heb, and adaline � Metode pengenalan pola menggunakan Hebb, Associative

Memory, BAM, dan MLP � Pattern recognition methods using Hebb, Associative Memory,

BAM, and MLP � Metode klasifikasi menggunakan MLP, RBF, jaringan recurrent,

dan LVQ, � Classification methods using MLP, RBF, Recurrent Network and

LVQ � Metode peramalan menggunakan MLP, RBF, dan Recurrent

Network � Forecasting methods using MLP, RBF, and Recurrent Network � Metode clustering menggunakan Kohonen SOM dan SVM � Clustering methods using Kohonen SOM and SVM � Metode Optimasi menggunakan Kohonen, dan Hopfield � Optimization methods using Kohonen and Hopfield


� Fausett,L, Fundamentals of Neural Networks,Prentice Hall, New Jersey, USA, 1994.

� Hassoum, MH, Fundamental of Artificial Neural Networks, MIT, 1995.

� Bishop, C, Neural Networks for Pattern Recoqnitions, Oxford

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University Press, 1996 � Duda, RO, Hart, PE, Stork, DG, Pattern Classification, John Wiley

and Sons, 2001 � Stork, DG and E. Yom-Tov, Computer Manual in MATLAB to

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


SM 092202: OPTIMASI DINAMIS (MATA KULIAH PILIHAN) SM 092202: DYNAMICS OPTIMIZATION (ASSORTED COURSE TITLE) Credits: 3 sks / credits unit Semester: II


� Memberikan pemahaman kepada mahasiswa tentang optimisasi dan aplikasinya

� To provide the student with an understanding of the optimization and their applications








� Pengantar desain � Introduction to Design, � Perumusan Masalah desain opt8imum � Optimum Design Problem Formulation, � Metode optimasi grafis � Graphical Optimization Method,

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� Konsep desain optimum � Optimum Design Concepts, � Metode Numerik untuk desain optimum tak terkendala � Numerical Methods for Unconstrained Optimum Design, � Metode Numerik untuk desain optimum terkendala � Numerical Methods for Constrained Optimum Design


Arora, J.S. Introduction to Optimum Design, Elsevier Academics Press, 2004.

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


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


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

� 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




� Mampu mengembangkan Matematika dan Terapannya � Able to develop Mathematics and its applications

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� Mampu mengimplementasikan kerangka berfikir matematis untuk merancang, menganalisis, dan mengevaluasi pemecahan masalah nyata



� Pengantar sistem logistic � Introduction of logistics system � Meramalkan kebutuhan logistic � Forecasting logistics demand � Merencanakan jaringan logistic � Planning logistics networks � Menyelesaikan masalah manajemen persediaan � Solving inventory management problem � Merancang dan mengoperasikan gudang � Design and operating a warehouse � Merancang dan mengatur angkutan transportasi jarak dekat dan

jauh � Design and manage short/long haul transportation


� Ghiani, G, Laporte, G and R. Musmanno, An Introduction to Logistics Systems Planning and Control, John Wiley and Sons, Ltd, 2004

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


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


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

To provide the student with an understanding of the graph theory as a mathematical model for solving mathematical problem

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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.


� F. Hanary, ”Graph Theory”, Addison-Wesley Publishing Co Inc., Massachussets USA, 1969

� Deo Narscyh, “Graph Theory with Applications to Engineering and computer science Preslitice Hall Inc., Englewod Cliffs, N.J., USA

� I Ketut Budayasa, “Teori Graph and Aplikasinya”, Unesa University Press, 2007


SM 092208: DISPERSI ATMOSFIR (MATA KULIAH PILIHAN) SM 092208: ATMOSPHERIC DISPERSION (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: II


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

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

KOMPETENSI/ � Mampu mengikuti perkembangan Matematika, Sains dan Teknologi

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COMPETENCY � Able to follow development of Mathematics, science and technology





� Pengangkutan skalar pada Atmosfir � Scalar Transport in the Atmosphere � Proses-proses pengangkutan � Transport Processes � Lapisan batas atmosfir � The Atmospheric Boundary Layer � Sumber-sumber titik penghasil polutan yang kontinyu � Continuous Point Sources of Pollutant � Dispersi pada lingkungan nyata � Dispersion in Real Environments � Kepulan Asap Gauss dari cerobong yang tinggi � Gaussian Plumes from High Chimneys � Deposisi � Deposition � Tipe-tipe dari model dispersi atmosfir � Types of Atmospheric Dispersion Models � Reaksi-reaksi kimiawi dari polutan yang ada di atmosfir � Chemical Reaction of Atmospheric Pollutants � Pembaganan pada Penyelesaian Numerik � Numerical Schemes


� Barrat, R., Atmospheric Dispersion Modelling, 1st Edition, Earthscan Publications, 2001

� Colls, J., Air Pollution, 1st Edition, Spon Press (UK), 2002 � European Process Safety Centre, Atmospheric Dispersion, 1st

Edition, Rugby: Institution of Chemical Engineers, 1999 � Schnelle, K.B. and Dey, P.R., Atmospheric Dispersion Modeling

Compliance Guide, 1st Edition, McGraw-Hill Professional, 1999 � Turner, D.B., Workbook of Atmospheric Dispersion Estimates: An

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

� Zannetti, P., Air pollution modeling : theories, computational methods, and available software, Van Nostrand Reinhold, 1990

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SM 092210: KECERDASAN BUATAN (MATA KULIAH PILIHAN) SM 092210: ARTIFICIAL INTELLIGENCE (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: III


� 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.

� 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.








� konsep kecerdasan buatan, � concept of artificial intelligence � teknik penyelesaian masalah menggunakan kecerdasan buatan � problem-solver technique using artificial intelligence � teknik pencarian, representasi pengetahuan, ketidakpastian � searching technique, knowledge representation, uncertainty � sistem pakar, and sistem pakar fuzzy � expert system and fuzzy expert system � algoritma genetika dan pemrograman genetika � genetics algorithms and genetic programming � particle swarm optimization dan algoritma koloni semut � particle swarm optimization and ant koloni algorithms

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� Stuart J. Russel and Peter Norvig, Artificial Intelligence A Modern Approach, McGrawHill, 2003

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

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


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


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

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


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

� The Students can use conservation laws, phenomenological and physical principles to make mathematical models of systems

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

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

� Mahasiswa mampu menganalisis keterkontrolan dan keteramatan dari sistem

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

� Mahasiswa mampu menganalisa perilaku input-output dari sistem

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

� Mahasiswa mampu menerapkan keterkontrolan sistem untuk menstabilkan sistem

� The students able to apply controllability of system to stabilize the systems

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� Mahasiswa mampu menetapkan kriteria kestabilan dari sistem

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


� Model-model matematika � Mathematical Models � Pengantar teori ruang keadaan � Introduction to State Space Theory � Teori stabilitas � Stability Theory


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

� Olsder G.j. and J.W. van der Woude, “Mathematical Systems Theory”, Delft Uitgavers Maatschappij, 1994.

� Hinrichsen D. and T. Pritchard “ Mathematical Systems Theory I Modelling, State Space Analysis, Stability and Robustness”, Springer Verlag ,2004


SM 092214 ASIMILASI DATA SM 092214 DATA ASSIMILATION Credits: 3 sks / credits unit Semester: 2


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.


� Mahasiswa mengerti metode asimilasi data dan model-model sistem dimana metode asimilasi data dapat digunakan.

� Mahasiswa mampu menjelaskan beberapa metode estimasi dan perkembangan metode asimilasi data.

� Mahasiswa dapat menerapkan asimilasi data pada model dinamik stokastik dan deterministik

� Mahasiswa mampu menjelaskan dan menerapkan berbagai perkembangan algoritma filter Kalman dalam asimilasi data.

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� The students understand about data assimilation method and where it’s can be applied.

� The students can explain several estimation methods and the pathways into data assimilation

� The students can apply data assimilation to dynamical stochastic/deterministic model

� The students can explain and apply the developing of Kalman filter as data assimilation method.


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

� Model-model yang digunakan dalam asimilasi data � Beberapa metode asimilasi data: Model statis stokastik, model

dinamik deterministic, model dinamik stokastik � Beberapa perkembangan algoritma Kalman Filter: Extended

Kalman Filter, RRSQRT filter, Ensemble Kalman Filter, Hibrid filter

� Studi kasus penerapan asimilasi data � Data assimilation: forecasting, modeling, observations,

sensitivity analysis � Modeling in data assimilation � Some of data assimilation methods: stochastic static model,

deterministic dynamic model, stochastic dynamic model � The advantage of Kalman filter: extended Kalman filter,

RRSQRT filter, Ensemble Kalman Filter, Hibrid filter � Case studies


� LEWIS, J.M., LAKSHMIVARAHAN, DHALL, S.K., 2006, DYNAMIC DATA ASSIMILATION: A LEAST SQUARES APPROACH, CAMBRIDE

� KALNAY, 2003, ATMOSPHERIC MODELING, DATA ASSIMILATION AND PREDICTABILITY, CAMBRIDGE


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

TUJUAN PEMBELAJARAN/

� Mahasiswa mengerti secara umum aljabar max plus dan notasinya, teori spektral, perilaku kualitatif periodik dan asimtotik, dan vektor siklus waktu.

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� 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.


� Mahasiswa mampu menerapkan aljabar maxplus di masalah nyata

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

� Mahasiswa mampu mampu mendapatkan nilai eigen dan vektor eigen dari matriks-matriks irreducible dan reducible

� The students able to find eigenvalues and eigenvectors of irreducible an reducible matrices.

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

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


� Aljabar Max-Plus � Max-Plus Algebra � Teori Spektral � Spectral Theory � Perilaku periodik dan vektor siklus waktu � Periodic behavior and the cycle-time vector � Perilaku kualitatif asimtotik � Asympotic Qualitative Behavior � Prosedur numerik dari nilai eigen matriks irreducible dan

reducible � Numerical Procedure of eigenvalues of irreducible and

reducible matrices � Introduction to Petri Nets


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

� 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

� 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 C.G. Cassandras and Stephane Lafortune, Introduction to Discrete Event Systems, Second Edition, Springer, 2008

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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


� Matakuliah komputasi dinamika fluida ini membahas tentang penggunaan komputer dan teknik numerik untuk menyelesaikan permasalahan yang berkaitan dengan aliran fluida

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








� Persamaan aliran fluida

� Fluid flow equation

� Persamaan Pengangkutan Skalar

� Scalar transport equation

� Persamaan momentum

� Momentum equation

� Turbulen

� Turbulence

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� Model Turbulen dalam KDF

� Turbulence modeling on the CFD

� Proses Komputasi Dinamika Fluida

� The Computational Fluid Dynamics Process


� Anderson, J. D. Jr., Computational Fluid Dynamics (The Basics with Applications), International Edition, New York, USA: Mc Graw-Hill, 1995

� Hoffmann, K. A. and Chiang, S. T., Computational Fluid Dynamics For Engineers, Wichita, USA: Engineering Education System, 1995

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

� Welty, J.R., et al., Fundamentals of Momentum, Heat and Mass Transfer, 3rd Edition, New York, USA: John Wiley & Sons, Inc., 1995

� 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.

� Tu, J.Y., Yeoh, G.H. and Liu, G.Q., Computational Fluid Dynamics-A Practical Approach, Oxford, UK: Butterworth-Heinemann Publications, 2008

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


SM 092205: KONTROL OPTIMUM (MATA KULIAH PILIHAN) SM 092205: OPTIMAL CONTROL (ASSORTED COURSE TITLE) Credits: 3 sks / credits unit Semester: 3

TUJUAN � Memberikan kepada mahasiswa pemahaman tentang masalah

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PEMBELAJARAN/ LEARNING OBJECTIVES

control optimal, pemodelan, aplikasi, simulasi dan komputasi

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








� Review kalkulus variasi � Review calculus of variation, � Kontrol optimal: system waktu diskrit dan system waktu

kontinyu � optimal control: Discrete-time systems and continuous-

time systems, � Kontrol optimal terkendala dan tak terkendala � unconstrained and constrained optimal control, � waktu akhir tetap dan bebas � fixed and free final time, � Aplikasi dan simulasi � application and simulation, � metode langung dan tak langsung � direct and indirect method, � Komputasi control optimal � computational optimal control.


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.

� Kamien, ML and Schwartz, N.L., Dynamic Optimizatio, North-Holland, Amsterdam, 1993.

� Lewis F., Optimal Estimation, John Wiley & Sons, Singapore, 1986.

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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


� Menyiapkan mahasiswa pemahaman topic-topik saat ini tentang pemodelan dan simulasi

� To provide the student with an understanding of the current

research topic in modelling and simulation








� 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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SM 092303 ANALISIS FUNGSIONAL SM 092303 FUNCTIONAL ANALYSIS Kredit: 3 sks Credits: 3 credits unit Semester: I


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.


� Dapat mengenali ruang Banach dan ruang Hilbert, berserta sifat-sifat utamanya.

� Dapat menunjukkan sifat-sifat operator linear terbatas, operator kompak, dan dapat membuktikan sifat-sifat utama operator kompak.

� Dapat membuktikan kelengkapan ruang Lp, dan mengenal penerapnnya.

� Able to identify Banach spaces and Hilbert spaces, and address

their main properties. � Able to show the main properties of bounded linear operators and

compact operators, and prove the fundamental properties of compact operators.

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


� Ruang Banach dan ruang Hilbert: pelengkapan, operator terbatas, jumlahan langsung, basis ortonormal, jumlahan ortogonal.

� Operator-operator kompak: definisi dan sifat-sifat pokok, teorema spektral untuk operator simetrik kompak.

� Integrasi Lebesgue: fungsi terukur, integral Lebesgue, pengertian “hampir dimana-mana”, ruang Lebesgue Lp, kelengkapan ruang Lp.

� Dual dari Lp: dekomposisi ukuran, ukuran kompleks, dual dari Lp

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

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

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

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


� 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.


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


� Menyiapkan mahasiswa pemahaman topic-topik saat ini tentang pemodelan dan simulasi

� To provide the student with an understanding of the

current research topic in modelling and simulation





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SM 092213: MULTI-KRITERIA OPTIMUM (MATA KULIAH PILIHAN) SM 092307: MULTICRITERIA OPTIMIZATION (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: I


� Mahasiswa mampu membuat model keputusan dalam menyelesaikan masalah yang berkarakteristik multicriteria secara optimal

� Student able to model decision making to solve problem which have optimal multicriteria characteristic








� Klasifikasi masalah multikriteria � Efisiensi dan nondominansi � Metode jumlahan terbobot

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� Teknik skalarisasi � Metode non skalarisasi � Multikriteriapemrograman linier � Metode multi objektif simplex � Multiobjektive criteria optimisasi


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

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


SM 092215: ANALISIS TIME SERIES (MATA KULIAH PILIHAN) SM 092215: TIME SERIES ANALYSIS (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: III


� Kuliah ini mendiskusikan karakteristik dari time-series, dasar-dasar regresi, teknik untuk data time series, pemodelan univariate ARIMA, proses GARCH, dan multivariate ARMAX.

� 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.








� Karakteristik dari time series � characteristics of time series � Pengantar konsep-konsep dasar dari model plot waktu

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� introducing the fundamental concepts of time plot models � Latar belakang dalam regresi � background in regression � teknik-teknik untuk data time-series � techniques for time series data dan nonstatsioner � pemodelan univariate ARIMA � univariate ARIMA modeling � proses-proses GARCH, model threshold, regresi dengan error-

eror autokorelasi, regresi tundaan, pemodelan fungsi alih � GARCH processes, threshold models, regression with

autocorrelated errors, lagged regression, transfer function modeling

� Model-model multivariate ARMAX � multivariate ARMAX models.


� Kirchgässner G and J. Wolters, Introduction to Modern Time Series Analysis, Springer-Verlag, Berlin, 2007

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

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


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


� Mahasiswa mampu menerapkan matematika dalam menganalisis resiko dalam setiap pengambilan keputusan.

� Student able to apply mathematics to risk analysis on decision

making

KOMPETENSI/ � Mampu mengikuti perkembangan Matematika, Sains dan

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COMPETENCY Teknologi � Able to follow development of Mathematics, science and

technology � Mampu mengembangkan Matematika dan Terapannya � Able to develop Mathematics and its applications � Mampu mengimplementasikan kerangka berfikir matematis




� Resiko dan analisis keputusan � Risk and decision analysis � Proses analisis keputusan � Decision analysis process � Kebijakan keputusan � Decision policy � Utilitas dan keputusan multi kriteria � Utility and multicriteria decision � Pohon keputusan � Decision tree � Penetapan dan bias � Judgment and bias � Menghubungkan resiko � Relating risk � Stochastics variance


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

2004 � John Schuyler, Risk and Decision Analysis in Projects, Project

Managemet Institute, Pennsylvania USA, 2001


SM 092219: SISTEM FUZZY (MATA KULIAH PILIHAN) SM 092219: FUZZY SYSTEM (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: III

TUJUAN PEMBELAJARAN/

� Memberikan pengetahuan tentang kenapa sistem fuzzy, matematika sistem fuzzy, operasi pada sistem fuzzy, relasi fuzzy, variable linguistic, logika fuzzy, pengambilan

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LEARNING OBJECTIVES

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

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








� Kenapa sistem fuzzy? � Why fuzzy system? � Matematika Himpunan Crsip vs Fuzzy � Mathematics Crisp vs Fuzzy Set � Fungsi keanggotaan � Membership function � Operasi-operasi pada himpunan fuzzy � Operation on Fuzzy Set � Variabellinguistic � Linguistic Variables � Relasi fuzzy, dan Logika Fuzzy � Fuzzy relation and fuzzy logic � Model-model pengambilan keputusan fuzzy � Models of fuzzy decision making � Forecasting dan clustering fuzzy � Fuzzy forcasting and clustering


� Buckley J, and E. Eslami, An Introduction to Fuzzy Logic and Fuzzy Sets, Physica Heidelberg, 2001,

� Klir, GJ and B. Juan, Fuzzy Set and Fuzzy Logic, Prentice Hall, New Jersey, 2001

� Zimmerman H.J, Fuzzy Set Theory and Its Applications, Kluwer Academic Publisher, 1996.

� Zadeh, LA., Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers , Kluwer Academic Publisher, 1996

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SM 092221: PENGOLAHAN CITRA (MATA KULIAH PILIHAN) SM 092221: IMAGE PROCESSING

(ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: I


� Mahasiswa mampu memahami konsep dasar dari pengolangan citra digital dan menerapkannya ke aplikasi yang lebih kompleks

� Students are able to comprehend basic concepts of digital

image processing and apply it to more complex application.








� Konsep dasar dari pemrosesan citra � The basic steps of image processing � Elemen system DIP, model citra sederhana, kuantisasi dan

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

sampling, � Transformasi Fourier, transformasi Fourier Diskrit 2D � Fourier transformation, 2D Discrete Fourier Transforms � Manipulasi citra: model warna, manipulasi RGB, metode

frekuensi dan spasial � Image Manipulation: Color model, RGB manipulation, Frequency

and spatial method, � Transformasi geometri � Geometry Transforms, � Perbaikan citra � Image Enhancement,

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� Segmentasi citra � Image Segmentation, � Pengantar pola � Introduction to pattern, � Kompresi citra � Image compression.


� Go Rafael C. Gonzalez and Richard E. Woods, Digital Image Processing, Addison Wesley. 1993

� 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


SM 092209: ANALISIS DATA SURVIVAL (MATA KULIAH PILIHAN) SM 092209: SURVIVAL DATA ANALYSIS (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: I


� Mahasiswa mampu menganalisis data daya survive dengan beberapa pendekatan model

� Students are able to analyze survival data with some

model approach







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� Pengantar analisis survival � Introduction to Survival Analysis � Kurva survival Kaplan-Meier dan Uji log rank � Kaplan–Meier Survival Curves and the Log–Rank Test . � Model bencana proporsional Cox dan karakteristiknya � The Cox Proportional Hazards Model and Its

Characteristics � Mengevaluasi bencana proporsional � Evaluating the Proportional Hazards � Prosedur berjenjang Cox � The Stratified Cox Procedure � Perluasan daribnecana proporsional Cox � Extension of the Cox Proportional Hazards � Model-model Survival Parametrik � Parametric Survival Models � Analisis Survival Kejadian berulang � Recurrent Event Survival Analysis � Komptensi Analisis resiko survival � Competing Risks Survival Analysis


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

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

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


SM 092225: OPTIMASI HEURISTIK (MATA KULIAH PILIHAN) SM 092225: HEURISTICS OPTIMIZATION (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: I


� Mahasiswa mampu memahami metode-metode heuristik dan mengimplementasikannya untuk menyelesaikan masalah optimasi

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

KOMPETENSI/ � Mampu mengikuti perkembangan Matematika, Sains dan Teknologi

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COMPETENCY � Able to follow development of Mathematics, science and technology





� Simulated Annealling � Scatter Search � Tabu Search � Evolutionary Algorithms � Genetics Algorithms and Genetics Programming � Memetics Algorithms � Ant Colony Algorithms � Simulated Annealling


� Petrowski J.D. and P.S.E. Taillard, Metaheuristics for Hard Optimization, Springer-Verlag Berlin Heidelberg, 2006

� Glover F. and Kochenberger G.A., Hand Book of Metaheuristics, Kluwer Academic Publishers, 2003

� 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


SM 092227: OPTIMASI KOMBINATORIAL (MATA KULIAH PILIHAN) SM 092227: COMBINATORIC OPTIMIZATION (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: I


� Memberikan pengetahuan kepada mahasiswa prinsip matematika untuk memodelkan dan mengembangkan penyelesaian optimal permasalahan combinatorial

� To provide the student mathematical principles to modelling

and developing optimal solution combinatorial problems.

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� Polytopes and Linear Programming � Matroids and Greedy Algorithm � Minimum-Weights Dipaths � Matroids Intersection � Matching � Networks Flow and Cuts � Cutting Planes for Integer Programming � Branch and Bound for discrete optimization � Optimizing Submodular Function


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

� Jens Gottlieb and Günther R. Raidl, Evolutionary Computation in Combinatorial Optimization, Springer-Verlag Berlin Heidelberg, 2006

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SM 092229: KAPSEL OPERATIONS RESEARCH (MATA KULIAH PILIHAN) SM 092229: SELECTED TOPICS OF OPERATIONS RESEARCH (ASSORTED COURSE TITLE) Credits: 3 sks / credits unit Semester: III


� Menyiapkan mahasiswa pemahaman topic-topik saat ini tentang riset operasi

� To provide the student with an understanding of the current research topic in Operations Research












SM 092231: GRID COMPUTING (MATA KULIAH PILIHAN)

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SM 092231: GRID COMPUTING (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: III


� Mahasiswa mampu mengimplementasikan komputasi matematika menggunakan konsep grid computing.

� Student able to implemented mathematical /numerical

computation using grid computing concept








� Definisi grid komputing � Definition of grid computing � Manajemen data � Data management � Penjadwalan grid dan layanan informasi � Grid scheduling and information services � Keamanan dalam grid computing � Security in grid computing � Grid middleware � Grid middleware � Tinjauan arsitektur dari poyek grid � Architectural overview of grid project � Metode monte carlo � Monte Carlo method � Implementasi pada terapan persamaan differensial parsial � Implementation on applied partial differential equations


� Magoules F, Pan J, Tan KA, and A. Kumar, Introduction to Grid Computing, Chapman & Hall Book, 2009

� Foster, I and Kasselman, The Grid 2, Elsevier, 2004

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SM 092233: DATA MINING DAN PENGENALAN POLA

(MATA KULIAH PILIHAN) SM 092233: DATA MINING AND PATTERN

RECOQNITION (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: III


� Memberikan pengetahuan dalam melakukan eksplorasi data

besar untuk mendapatkan pola, trends, dan anomali-anomali dengan model-model quantitative, merubah data menjadi informasi dan merubah informasi menjadi pengetahuan.

� Finding patterns, trends, and anomalies in these datasets, and

summarizing them with simple quantitative models. Turning data into information and turning information into knowledge.








� Data Mining and machine learning � Input: concepts, instances, and attributes � Output: Knowledge representation � statistical modelling, � decision tree, � association rules, � linear model,

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� nearest neighbour, � clustering, � Bayesian networks,


� Weitten I.A .and E.Frank, Data Mining: Practical Machine Learning Tools and Techniques, Elsevier Inc, 2005

� Ho Tu Bao, Introduction to Knowledge Discovery and Data Mining, manuscript from Institute of Information Technology, National Centre for Natural Science and Technology, Taiwan, 2004

� Dasu T. and T. Johnson , Exploratory Data Mining and Data Cleaning, Johm Wiley & Sons, 2003


SM 092235: KAPSEL ILMU KOMPUTER (MATA KULIAH PILIHAN) SM 092235: SELECTED TOPICS OF COMPUTER SCIENCES (ASSORTED COURSE TITLE) Credits: 3 sks / credits unit Semester: III


� Menyiapkan mahasiswa pemahaman topic-topik saat ini tentang ilmu komputer

� To provide the student with an understanding of the

current research topic in computer sciences









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SM 092237: INVERS PROBLEM (MATA KULIAH PILIHAN) SM 092237: INVERSE PROBLEMS (ASSORTED COURSE TITLE) Credits: 3 SKS / 3 Credit units Semester: III


� Mahasisiwa mampu menyelesaikan masalah nyata dengan menerapkan metode invers problem

� Student able to solve real world problem using inverse problem








� Diskrit invers problem umum � The general discrete inverse problem � Metode monte carlo � Monte Carlo Method � Kriteria least square � The least square criterion � Kriteria nilai mutlak dan minimax � Least absolute value criterion and minimax criterion � Fungsional inverse problem

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� Functional inverse problem � Aplikasi invers problem � Aplication of inverse problem �


� Albert Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, Society for Industrial and Apllied Mathematics (SIAM), 2005

� Victor Isakov, Inverse Problem for Partial Differential Equations, Springer Verlag Berlin, 1998

� Aster A.C., Borchers B., and C.H. Thurber, Parameter Estimation and Inverse Problem, Elsevier inc, 2005


SM 0912239: RISET OPERASI LANJUT (MATA KULIAH PILIHAN) SM 0912239: ADVANCED OPERATION RESEARCH (ASSORTED COURSE TITLE) Credits: 3 sks / credits unit Semester: 3


� Memberikan pemahaman kepada mahasiswa teori dan aplikasi riset operasi untuk menyelesaikan masalah di industri

� To provide the student with an understanding of the theories and applications of the operations research to solve a problem at industries.



� Goal Programming, � Pemrograman multi objektif � Multi Objective Programming, � System antrean � Queuing system, � Teori permainan � Game theory, � simulasi � Simulation

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� Pemrograman non linier � Nonlinear Programming.


� Ravindran, A.R., Operations Research Methodologie, CRC Press, 2009.

� Taha, H.A., Operation Research an Introductio, 7th Edition Prentice Hall Pearson Education, Inc., New Jersey, 2003.

� Hiller & Lieberman, Introduction to Operations Research, Holden-Day Inc., California, 1996.

� Winson, Operation Research Applications and Algorithm, Duxbury Press Belmont, California, 1994.

[FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM]...

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