SYLLABUS MASTER OF MATHEMATICS

SYLLABUS MASTER OF MATHEMATICS

Departement of

Mathematics

Faculty of Science and Data Analytics Institut Teknologi Sepuluh Nopember

PROGRAMME LEARNING OUTCOMES (PLO)

PLO-1 [C3] Students are able to solve mathematical problems by applying

fundamental mathematical statements, methods, and computations

PLO-2

[C4] Students are able to analyze mathematical problems in one of

the fields: analysis, algebra, modeling, system, optimization or

computing sciences

PLO-3

[C5] Students are able to work and research collaboratively on

mathematical problems within either the area of pure mathematics

or applied mathematics or computing sciences

PLO-4 Students are able to communicate and present mathematical ideas

with clarity and coherence, both written and verbally

PLO-5 Students are able to make use of the principles of long life learning

to improve knowledge and current issues on mathematics

PLO-6 Students are able to demonstrate religious attitude and tolerance

PLO-7 Students are able to demonstrate an attitude of responsibility and

commitment to law enforcement, ethics, norms for community and

environmental sustainability

SYLLABUS

List of Master Program Courses

SEMESTER 1

No. Course Code Course Name Credit

1. KM185101 Module Theory 3

2. KM185102 Functional Analysis 3

3. KM185103 Mathematical Modeling 3

4. KM185104 Numerical Computing 2

Total credits 11

SEMESTER 2


1. KM1852xx Compulsary Courses 6

2. KM1852xx Elective Courses 3

Total credits 9

SEMESTER 3


1. KM1853xx Elective Courses 8

Total credits 8

SEMESTER 4


1. KM185401 Thesis 8

Total credits 8

List of Compulsary Courses

SEMESTER 2

No. Code Compulsary Courses Credits

1. KM185211 Approximation Theory 3

2. KM185212 Max-Plus Algebra 3

3. KM185221 Dynamical Systems 3

4. KM185222 Stochastics Calculus 3

5. KM185231 Computational Algorithm 3

6. KM185232 Mathematics of Machine Learning 3

List of Elective Courses

SEMESTER 2

No. Code Elective Courses Credits

1. KM185271 Discrete Transformation 3

2. KM185272 Formal Verification 3

3. KM185273 Systems and Controls 3

4. KM185274 Computational Fluid Dynamics 3

5. KM185275 Dynamical Optimization 3

6. KM185276 Financial Mathematics 3

7. KM185277 Digital Image Processing and Analysis 3

SEMESTER 3

No. Code Elective Courses Credits

1. KM185372 Mathematical Biology 3

2. KM185373 Data Assimilation 3

3. KM185374 Computational Biology 3

4. KM185375 Mathematics of Derivatives 3

5. KM185376 Risk Analysis 3

6. KM185377 Graph Algebra 3

7. KM185378 Theory of Computing 3

8. KM185379 Wavelet and Applications 3

9. KM185380 Advanced Partial Differential Equations 2

10. KM185381 Inverse Problems 2

11. KM185382 Fuzzy Systems 2

12. KM185383 Graph and Applications 2

13. KM185384 Topics of Applied Analysis 2

14. KM185385 Topics of Computing 2

15. KM185386 Topics of Mathematical Modeling 2

16. KM185387 Topics of Applied Algebra 2

17. KM185388 Topics of Optimization 2

Detail of Courses

COURSES

Name Subjects : Module Theory

CS Code : KM185101

Credit : 3

Semester : 1

COURSE DESCRIPTION

This course presents an advanced study of a fundamental concept of Linear

Algebra. The discussion is emphasized on the aspects of Algebra that is

commutative group, ring and module theory. Furthermore, some materials

will be theory Module Provided for future understanding for students who

will have special abilities in the field of Algebra and other related fields or

applications that need them. Assessment of learning outcomes is done

through written evaluations, classroom discussions and student presentations

and releases them in paper format.

ACHIEVEMENTS GRADUATES CHARGED LEARNING COURSE

PLO 1 Students are able to solve mathematical problems by applying


ACHIEVEMENT OF LEARNING COURSES

A mature student is able to develop math and writing mathematical proof

by default.

Students are able to develop an understanding of the concept and be able

to draw conclusions pituitary and in particular the theory of linear

algebra ideas for module theory and computational problems.

Students are able to appreciate the importance of understanding the

structure of algebra to a higher-level concepts.

Students can create awareness kususnya symbolic thinking within the

framework of the theory of modules

Students have the capability to use its understanding and analyzing

models of mathematics, science and technology and other disciplines

related fields.

Students are able to develop an understanding matematematika

framework that supports science and technology, and mathematics as

well as communicate the results of the development of oral and written

comprehension.

SUBJECT

Commutative groups and subgroups

Commutative additive group Homomorpisma

Ring, homomorpisma ring, subring and ideal

Ideal Prima and Ideal Maximum

Quasi field

Single factorization area

Module and submodule

The set expander

Non Linear Element Torque and Annihilator

Modules and Module Quasi Homomorpisma

Free modules and modules Noetherian

Modules on the Main Ideal Regions

PRECONDITION

-

REFERENCES

1. Subiono., "Lecture Notes: Module Theory", Mathematics Department,

FMKSD-ITS, 2018.

2. Adnan Tercan and Canan C. Yücel, "Module Theory, Extending

Modules and its generalizations", Birkhäuser, 2016

3. Ernest Shult and David Surowski, "Algebra, A Teaching and Source

Book", Spriger, (2015)

4. Paul E. Bland, "Ring and Their Modules", Walter de Gryter GmbH &

Co., Berlin / Newyork, (2011)

5. Steven Roman, "Avanced Linear Algebra, Third Edition", SPRINGER,

(2008).

6. WA Adkins and SH Weintraub, "Algebra An Approach via Module

Theory", SPRINGER-Verlag, (1999)

7. DG Northcott, FRS, "Lessons on Rings, Modules and multiplicities",

Cambridge at the University Press, (1968)

LIBRARY SUPPORT

Paul A. Furmann, "A polynomial Approach to Linear Algebra, Second

Edition", SPRINGER, (2012)

COURSES

Name Subjects : Functional Analysis

CS Code : KM185102

Credit : 3 credits

Semester : 1

COURSE DESCRIPTION

In this course, it is studied about concept of metric space, topology, norm

space and inner product such that the student can analyze the convergence of

series function, bounded and continuity. It is also studied how to prove some

theorem in those spaces. Bounded and continuity operator in those spaces are

studied.


PLO-1 Students are able to solve mathematical problems by applying

fundamental mathematical statements, methods, and

computations


The student able to explain the characteristic of vector space, metric

space, norm space and inner product space.

The student able to explain and analyze the convergence of sequences,

open set and function continuity.

The student able to prove the relevant theorems on those spaces.

The student able to define operator and analyze the bounded and

continuity of operator

SUBJECT

Metric space

Norm space

Inner product space

Linear operator

PRECONDITION

-

REFERENCES

1. Yunus, M., Textbook of Functional Analysis, Department of

Mathematics ITS, 2014

2. Zeidler, E., Applied Functional Analysis, Springer Verlag, 1995

LIBRARY SUPPORT

-

COURSES

Name Subjects : Mathematical Modeling

CS Code : KM185103

Credit : 3 credits

Semester : 1

COURSE DESCRIPTION




computations

PLO-2 Students are able to analyze mathematical problems in one of the

fields: analysis, algebra, modeling, system, optimization or

computing sciences

PLO-3 Students are able to work and research collaboratively on




SUBJECT

PRECONDITION

REFERENCES

LIBRARY SUPPORT

COURSES

Name Subjects : Numerical Computing

CS Code : KM185104

Credit : 2

Semester : 1

COURSE DESCRIPTION

The course is a numerical computing that gives an opportunity to the

students to be able to solve the problems of numerical mathematics. This

course discusses about the error, interpolation, turnan andNumerical of

integration, ordinary differential equations (initial value problems), and

partial differential equations.




computations



computing sciences


Students are able to analyze errors and kekovergenannya of a numerical

solution.

Students are able to actively construct mathematical problem solving

algorithms with numerical approach

students can implement numerical approach to the programming

language MATLAB to solve the problems of mathematics.

Students are able to apply numerical approach to various

multidisciplinary applications of science and technology.

SUBJECT

Error Analysis: analyzing error and kekonvergenannya

Interpolation: polynomial Newton, Newton divided difference method,

Lagrange polynomial, linear and quadratic spline

Numerical derivative: Difference Method Forward / Backward /

Center, Newton-Cotes Rules, Richardson Extrapolation, derivatives

High Level

Numerical Integral: Rule Simpson, Simpson 3/8, Romberg method,

quadrature Gauss - Legendre

Numerical GDP: Euler method, Heun method, Runge-Kutta methods,

Methods Predictor - Corrector

Numerical PDP: implicit and explicit methods

PRECONDITION

-

REFERENCES

1. RL Burden and JD Faires, Numerical Analysis, 9th edition, Brooks-

Cole,

2. Atkinson Kendall and Weimin Han, Elementary Numerical Analysis,

2nd edition, John Wiley & Sons, Inc.

3. Steven Chapra and Canale, Numerical methods for engineering, 4th

edition, McGraw-Hill, 2002

LIBRARY SUPPORT

-

COURSES

Name Subjects : Approximation Theory

CS Code : KM185211

Credit : 3

Semester : 2

COURSE DESCRIPTION

This course discusses the main frame of approximation theory, with an

emphasis on classical topics related to polynomial and rational functions,

along with computational approaches. The main discussion begins from

Weierstass Approximation Theorem, which includes a discussion interpolan

Chebyshev, polynomials and Chebyshev series. Then on the best

approximation that includes the convergence function convergence

diferensiabel and analytic functions. While the last part will discuss topics

relating to spectral methods and accelerated convergence.




computing sciences


Being able to understand the main points of the classical approximation

theory as a basis approximation method development and application.

Being able to explain the advantages of some of the best approximation

method

Being able to apply some approximation methods in solving problems

related approximation.

SUBJECT

Approximation Theorem Weierstass

Best approximation

Spectral method

Convergence acceleration

PRECONDITION

- Functional analysis

- Numerical computing

REFERENCES

Trefethen, LN, Approximation Approximation Theory and Practice, SIAM,

2013

LIBRARY SUPPORT

Christensen, O. and Christensen, KL, Approximation Theory, Birkhauser,

2005

COURSES

Name Subjects : Max-Plus Algebra

CS Code : KM185212

Credit : 3

Semester : 2

COURSE DESCRIPTION

This course is presented on a study of a fundamental concept Algebra Max

Plus and development that is supertropical algebra. The discussion focused

on aspects of Theory and Applications. Furthermore, given the understanding

Petri net in general, especially the relationship with the max plus algebra and

given the ability to perform numerical computation in any discussion of using

Scilab Max Plus Algebra Toolbox. Problem-based discussion is an integrated

part in the study. Assessment of learning outcomes is done through an

evaluation board, presentations and discussion of learners in the classroom.




computing sciences


A mature student is able to develop math and writing mathematical

proofs by default

Students are able to appreciate the importance of understanding the

structure of algebra to a higher - level concepts.

Students can create awareness kususnya symbolic thinking within the

framework of algebra supertropical

Students are able to develop an understanding of the concept and be able

to draw conclusions and theories particularly pituitary max plus algebra

idea to issue a large scale computing system

Students have the understanding and the ability to use mathematical

models to analyze issues, particularly the issue of scheduling and other

disciplines related fields.

Students are able to develop an understanding matematika framework

that supports science and technology, and mathematics as well as

communicate the results of the development of understanding orally in

the form of presentations and writing standard in mathematics

SUBJECT

semiring

Petri Net

Algebra Super Tropical

PRECONDITION

Module theory

REFERENCES

1. Subiono. "Lecture Notes: Ajabar Max Plus and Applications",

Department of Mathematics FMKSD-ITS, 2018.

2. Subionoand Kistosil Fahim, On Computing Supply Chain Scheduling

Using Max Plus Algebra, Applied Mathematical Science, Journal for

Theory and Applications, vol. 10, no. 10, 477-486, 2016 DOI 10.12988

/ ams.2016.618.

3. Kistosil Fahim, Subiono and Jacob van der Woude, On a generalization

of power algorithms over max-plus algebra, DEDS, Discrete Event Dyn

Syst (2017) 27: 181-203, DOI 10.1007 / s10626-016-0235-4, Springer

Science + Business Media New York in 2017.

4. Subiono, "On Classes of Min Max Plus Systems and Their

Applications", PhD. Thesis, TU Delft, The Netherlans, (2000)

5. Olsder Gj, Heidegott B. and JW van der Woude, Maxplus at Work,

Modeling and Analysis of Synchronized System: A Course on Max-Plus

Algebra and ITS Applications, Princeton University Press, 2006

6. Subiono, and JW van Wounde, "Power Algorithms for (mas, +) - and

Bipartite (min, max, +) - Systems", Discreate Event Dynamic Systems:

Theory and Applications, Volume 10, pp 369-389, 2002

7. CG Cassandras and Stephane LaFortune, Introduction to Discrete Event

Systems, Second Edition, Springer, 2008

8. Peter Butkovic, "Max-Linear Systems: Theory and Algorithms",

Spriger 2010

9. Michel Gondran and Michel Minoux, "Graph, Dioids and Semirings,

New Models and Algorithms", Springer, 2008

10. Christos G. Cassandras and Stephane LaFortune, "Introduction to

Discrete Event Systems, Second Edition", Spriger 2008

11. James L. Peterson, "Petri Net Theory and the Modeling of Systems",

Printice Hall, Inc., 1981

LIBRARY SUPPORT

1. Dieky Adzkiya, "Building Petri Net Model of Traffic Lights and

simulation", Thesis Department of Mathematics ITS, (2008)

2. Peter Fendiyanto " Supervisory Control on Traffic Management

Systems at Airports Using Petri Net ", Thesis Department of

Mathematics ITS, (2016)

COURSES

Name Subjects : Dynamical Systems

CS Code : KM185221

Credit : 3

Semester : 2

COURSE DESCRIPTION

This course on study about the dynamic behavior of a system of ordinary

differential equations in the form of both linear and nonlinear in a way to

stability and bifurcation analysis system




computing sciences







Students are able to analyze the stability of linear dynamic systems and

nonlinear

Students are able to simplify the system by way of normalization and

establishment of centers manifold

Students are able to understand and prove the theorem to determine the

occurrence of bifurcation and the types

Students are able to analyze the stability of the system with delay

Students are able to identify the real problems in the form of a dynamical

system

SUBJECT

Stability

Bifurcation

PRECONDITION

-

REFERENCES

1. Wiggins, S. 2009, "Introduction to Applied Non-Linear Dynamical

System and Chaos- second edition", Springer-Verlag

2. Xiaoxin Liao, Wang, L. And Pei Yu, 2007, "Stability of System

Dynamics", Elsivier

LIBRARY SUPPORT

-

COURSES

Name Subjects : Stochastic Calculus

CS Code : KM185222

Credit : 3

Semester : 2

COURSE DESCRIPTION

This course provides the concept of stochastics process to learn the modern

financial theory. The topics include basic concept of probability, random

variables, discrete and continuous distributions, and Markov chain.

Subsequently, the course introduces the concept of martingale, Brownian

motion, and Ito calculus.




computing sciences


Students are able to learn the concept of probability, discrete stochastic

process and martingale,

Markov process and its applications, Brownian motion, and continuous

martingale.

Students are able to learn the concept of Ito calculus and its applications

in finance and other reas.

SUBJECT

Probability

Stochastic integral

Stochastic differential equations

PRECONDITION

Probability Theory

REFERENCES

1. Syamsuddin, "Financial Mathematics", Lecturer Notes

2. Brzezniak and Zastawniak, "Basic Stochastic Processes", Springer, 1999

3. Shreve, Steven, "Stochastic Calculus for Finance, a Continuous Time

Model", Springer, 2004

4. Medina and Merino, "Mathematical Finance and Probability, A Discrete

Introduction", Birkhauser Verlag, 2003

5. Kelbaner, FC, "Introduction to Stochastic Calculus with Applications",

Imperial College Press, 2005

LIBRARY SUPPORT

-

COURSES

Name Subjects : Computational Algorithm

CS Code : KM185231

Credit : 3 credits

Semester : 2

COURSE DESCRIPTION

These courses provide the ability to formulate and solve the problems of

mathematics and its applications to computational algorithms approach. In

addition, students will be able to implement it with Matlab and use the concept

given to reveal the back and / or communicate ideas related to the field of

mathematics either in writing or orally with individual and group performance

in teamwork.

The topics covered include basic concepts of design and analysis of

algorithms, the basic principles of matrix computation and optimization

algorithms. The learning model is done through the tutorial and discussion in

the classroom / lab. In addition to self-directed learning through tasks, learners

are directed to cooperate in group work. Assessment of learning outcomes is

done through an evaluation board, independent tasks, and the ability to write

and present a given task.




computing sciences


College student be able to formulate and solve the problems of

mathematics and its application with the approach of computational

algorithms and implement it with Matlab and use the concept given to

reveal the back and / or communicate ideas related to the field of

mathematics either in writing or orally to the performance of individuals

and in groups in teamwork.

Students are able to explain the concept of the design and analysis of

algorithms

Students are able to explain and implement the basic principles of

computational matrix

Students are able to explain and implement some optimization

algorithms

SUBJECT

Computing Matrix

Optimization algorithm

PRECONDITION

-

REFERENCES

1. Matrix Computation, 4th ed, Gene H. Golub and Charles F. Van Loan,

The Johns Hopkins University Press, 2012

2. Introduction to Algorithms, 3rd Edition, Thomas H. Cormen, CE

Leiserson, RL Rivest, MIT Press, 2009

LIBRARY SUPPORT

1. Computer Algorithms: Introduction to Design and Analysis, 3rd Edition,

Sara Baase and Allan Van Gelder, 2000.

COURSES

Name Subjects : Mathematics of Machine

Learning

CS Code : KM185232

Credit : 3

Semester : 2

COURSE DESCRIPTION




computing sciences


SUBJECT

Theory Mat / Stat for Machine Learning

Convexity algorithm

Learning algorithm

PRECONDITION

REFERENCES

LIBRARY SUPPORT

COURSES

Name Subjects : Discrete Transformation

CS Code : KM185271

Credit : 3

Semester : 2

COURSE DESCRIPTION




computing sciences


SUBJECT

Linear transformations

Fourier transformation

Wavelet transformation

PRECONDITION

REFERENCES

LIBRARY SUPPORT

COURSES

Name Subjects : Formal Verification

CS Code : KM185272

Credit : 3

Semester : 2

COURSE DESCRIPTION

In this course will be given an insight to students about the background and

verification processes on the system transition. In addition to theoretical

studies, students are also introduced to some of the software for the

verification of the model, such as SPIN or NuSMV. Study paper / paper on

the topic is presented in the form of discussions and presentations.




computing sciences


1. Students are able to explain the formal verification methods and models

system where formal verification methods can be applied.

2. Students are able to explain some of the methods of verification systems

and the development of a system of verification methods.

3. Students can apply the model checking system model transitions, both

theoretically and using software

4. Students are able to explain and apply various algorithms on system

verification.

SUBJECT

Understanding verification system: Why it is needed, the difference with

the simulation, the advantages of the methods of verification systems, the

boundaries of the verification system, the models used in the verification of

the system: the system transition, a few specifications that are commonly

used: linear-time property, linear temporal logic, computation tree logic, some

software for system verification: SPIN, NuSMV, case studies verify the

application of the system

PRECONDITION

-

REFERENCES

1. Baier, C. and Katoen, J-.P, 2008, Principles of Model Checking, The MIT

Press

2. Ben-Ari, M., 2008, Principles of the SPIN model of checkers, Springer

LIBRARY SUPPORT

-

COURSES

Name Subjects : Systems and Controls

CS Code : KM185273

Credit : 3

Semester : 2

COURSE DESCRIPTION

Systems and Control consist of Definition of the system, Principles of

Modeling, Linear Systems and Properties System, Input/Output Feedback

Control, Input/Output Representation, Optimal Control (LQR), and the

methods of control growing recently. In the process of learning in class

students will be given an understanding of problem identification and

reduction of mathematical models and represent into the form of the system,

then determine the appropriate controls with these problems. In addition to

self-directed learning through tasks, students are directed to cooperate in

group work. Assessment of learning outcomes is done through an evaluation

board, tasks and discussions in class activities.




computing sciences


Students are able to follow developments and apply linear systems and

optimum control and be able to communicate actively and properly

either oral or written.

Students are able to explain the basic principles and theory understood

further from dealing specifically with linear system and capable of

designing an appropriate control system.

Students are able to explain intelligently and creatively about the

significant role Optimum Linear Systems and Control in the field of

knowledge related clumps or other fields.

Students are able to present an understanding of science in the field of

Linear Systems and Control Optimum independently or in teamwork.

SUBJECT

The state space

MIMO systems

design Control

PRECONDITION

-

REFERENCES

1. Subiono., "Linear Systems and Optimal Control", Department of

Mathematics-ITS, 2014.

2. Frank L. Lewis, Draguna LV, Vassilis LS, "Optimal Control and

Estimation", Wiley and Son, New Jersey, Canada, Inc., (2012)

3. Olsder, GJ, "Mathematical System Theory", Fourth Edition, VSDD,

Delft in The Netherlands (2011)

LIBRARY SUPPORT

1. M. Gopal, "Modern Control System Theory", New Age International (P)

Limited, Publishers, (1993).

2. CT Chen, "Linear System Theory and Design", Fourth Edition, Oxford

University Press. (2012)

COURSES

Name Subjects : Computational Fluid

Dynamics

CS Code : KM185274

Credit : 3

Semester : 2

COURSE DESCRIPTION

Course computational fluid dynamics is about the computational aspects of

fluid dynamics.




computing sciences







Students understand, control and understanding of the fluid flow

equations.

Students are able to develop the transport scalar equations and

momentum.

Students are able to understand the basic concepts of turbulence.

SUBJECT

Fluid flow

flow modeling

Numerical solution of fluid flow problems

PRECONDITION

-

REFERENCES

Anderson, JDJ, 1995, Computational Fluid Dynamics (The Basics with

Applications), International Edition, Mc Graw-Hill, New York, USA.

LIBRARY SUPPORT

1. Anderson, JDJ, 1995, "Computational Fluid Dynamics (The Basics with

Applications) '', International Edition, Mc Graw-Hill, New York, USA.

2. Hoffmann, KA and Chiang, ST, 1995, "Computational Fluid Dynamics

For Engineers, Engineering Education System", Wichita, USA.

3. Shames, IH, 1992, "Mechanics of Fluid, 3rd Edition", Mc Graw-Hill,

New York, USA.

4. Welty, JR, et al., 1995, '' Fundamentals of Momentum, Heat and Mass

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

5. Wilkes, DJF, et al., 1995, "Fluid Mechanics, 3rd Edition", Longman

Publishers Singapore, Singapore.

COURSES

Name Subjects : Dynamical Optimization

CS Code : KM185275

Credit : 3 credits

Semester : 2

COURSE DESCRIPTION

Discussion subjects include an assessment of dynamic optimization basics of

calculus of variations, optimal control, modeling, application, simulation and

computing. In the learning process in the classroom learners will learn to

identify the real problems, modeling, and finish it. In addition to self-directed

learning through tasks, learners are directed to cooperate in group work and

write scientific papers in the form of paper.




computing sciences







Students are able to follow developments and apply mathematics and be

able to communicate actively and properly either oral or written

Students are able to explain the basic principles and further from the

theory that understands particularly with regard to dynamic optimization

Students are able to explain intelligently and creatively about the

significant role of optimization in the areas of knowledge related clumps

or other fields

SUBJECT

calculus of Variations

Optimal control

PRECONDITION

-

REFERENCES

A. Naidu, DS, "Optimal Control Systems '', CRC Press, 2002.

B. Subchan, S and Zbikowski, R., "Computational Optimal Control: Tools

and Practice", Wiley, 2009.

C. Lewis, F. and Syrmos Vassilis, "Optimal Control", John Wiley & Sons,

Singapore, 1995.

D. Suzanne Lenhart, John T. Workman, "Optimal Control Applied to

Biological Models", CRC Press, 2007.

E. Krasnov, ML, Makarenko, GI, and Kiselev, AI, Problems and Exercises

in the Calculus of Variations, MIR Publishers Moscow, 1975.

F. Bryson and Yu-Chi Ho, Applied Optimal Control: Optimization,

Estimation and Control, Taylor and Francis Group, 1975.

LIBRARY SUPPORT

1. Kamien, ML and Schwartz, NL, "Dynamic Optimization", North-

Holland, Amsterdam, 1993.

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

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https://www.amazon.com/Applied-Optimal-Control-Optimization-Estimation/dp/0891162283/ref=sr_1_1?s=digital-text&ie=UTF8&qid=1513045502&sr=8-1&keywords=Optimal+Control+Bryson

https://www.amazon.com/Applied-Optimal-Control-Optimization-Estimation/dp/0891162283/ref=sr_1_1?s=digital-text&ie=UTF8&qid=1513045502&sr=8-1&keywords=Optimal+Control+Bryson

COURSES

Name Subjects : Financial Mathematics

CS Code : KM185276

Credit : 3

Semester : 2

COURSE DESCRIPTION

This course provides theories and models of annuity, interest rate, and

portfolio investment. The modelling of annuity for various payment schemes

with related various interest rate models is presented. Then the development

of investment portfolio based on the annuity models is assigned for the

applications.






computing sciences







Students are able to understand and apply their mathematics ability to

build annuity models.

Students are able to understand and develop the loan repayment scheme

Students are able to learn and determine the bond value

Students are able to learn and develop the analysis of rate of return in

investments.

SUBJECT

Annuity

Loan repayment

Investment Portfolio

PRECONDITION

Calculus II

REFERENCES

1. Garrett, SJ, "An Introduction to the Mathematics of Finance '', Second

Edition, Elsevier, 2013

2. Broverman, Samuel, "Mathematics of Investment and Credit", 5th

Edition, ACTEX Publication 2010

3. Brigham, EF and Ehrhardt, MC, "Financial Management", Thomson

Southwestern

LIBRARY SUPPORT

-

COURSES

Name Subjects : Digital Image Processing and

Analysis

CS Code : KM185277

Credit : 3

Semester : 2

COURSE DESCRIPTION

Digital Image Analysis is a subject which contains the basic concepts of

applied mathematics for image processing and algorithms for image

processing. Basic math concepts covered include, namely of transformation

Fourier, wavelet transform and mathematical morphological. Image

processing techniques include enhancement, restoration, segmentation and

image compression.




computing sciences


Able to understand and develop concepts and basic techniques of image

processing

Able to understand and implement image processing algorithms with the

programming language.

Able to apply image processing techniques for image processing

applications more complex individually or in groups in the form of

presentations or papers.

SUBJECT

Image processing: image enhancement spatial and frequency domain,

image restoration

Image Segmentation: edge detection, segmentation methods

Image Analysis: feature extraction and classification

image compression

wavelet

PRECONDITION

-

REFERENCES

1. RC Gonzalez and RE Woods, "Digital Image Processing, Third

Edition", Pearson, 2008

2. John C. Russ, "The Image Processing Handbook, Sixth Edition", CRC

Press, 2011.

LIBRARY SUPPORT

1. Bhabatosh, Majumder, Dwijesh Dutta, "Digital Image Processing And

Analysis", Prentice Hall, 2006

2. Gonzalez, Woods, and Eddins, "" Digital Image Processing Using

MATLAB (DIPUM) ", Prentice Hall, 1st edition, 2004.

COURSES

Name Subjects : Mathematical Biology

CS Code : KM185372

Credit : 3

Semester : 3

COURSE DESCRIPTION




computing sciences


1. Able to understand the problem in the form of a continuous population

models -diffusi reaction and analyze the behavior of the system

2. Able and mastered the meaning pupolasi interaction as a function of the

transmission in the dispersion model

3. Being able to construct models of the phenomena discrete object of

observation.

4. Being able to make project-related research and to publish reaction

model –diffuse

SUBJECT

Continuous Population Model

Discrete Population Model

Population Interaction Model

PRECONDITION

system dynamics

REFERENCES

1. Marco Di Francesco 2010. "Mathematical models in life science"

2. Eduardo D. Sontag 2006, "Lecture Notes in Mathematical Biology"

Rutgers University.

3. DW Hughes, JH Merkin, R. Sturman, 2004, "Lecture Notes in Analytic

Solutions of Partial Differential Equations" School of Mathematics,

University of Leeds.

4. F Brauer C. -Chavez, 2012. "Mathematical Models in Population

Biology and Epidemiology", Texts in Applied Mathematics, Springer

Science + Business Media

LIBRARY SUPPORT

-

COURSES

Name Subjects : Assimilation Data

CS Code : KM185373

Credit : 3 credits

Semester : 3

COURSE DESCRIPTION

In this course is studied about definition of data assimilation, comparing

between classical estimation and data assimilation, the application of data

assimilation to estimate the stochastic dynamical system.




computing sciences


The student able to explain data assimilation method and the models that

can data assimilation applied.

The student able to explain some methods of estimation and the data

assimilation development

The student able to apply data assimilation method on stochastic

dynamical system and deterministic dynamical system.

The student able to explain and apply some development of Kalman

filter algorithm as one of data assimilation method.

SUBJECT

Classical Estimates

Estimation of Stochastic Models

Development of Data Assimilation Methods

Applied methods of data assimilation

PRECONDITION

-

REFERENCES

1. Lewis, JM, Lakshmivarahan, Dhall, SK 2006, "Dynamic Data

Assimilation: A Least Squares Approach", Cambride

2. Kalnay 2003, "Atmospheric Modeling, Data Assimilation And

Predictability", Cambridge

LIBRARY SUPPORT

-

COURSES

Name Subjects : Computational Biology

CS Code : KM185374

Credit : 3

Semester : 3

COURSE DESCRIPTION

Computer applications increasingly important issues in the field of

bioinformatics and offers a lot of challenges from the perspective of the

computing process. In this course, students will gain the ability to formulate

problems of bioinformatics, particularly sequence analysis into the form of a

computational model and solve it with the help of software. In addition,

students will learn some of the alternative settlement in sequence analysis. To

deepen understanding, students will implement it with Matlab and use the

concept given to reveal the back and / or communicate ideas related to the

field of mathematics either in writing or orally with individual and group

performance in teamwork.

The topics covered include sequence alignment problem solving, stochastic

modeling for the analysis of mutations, super pairwise alignment and multiple

alignment and phylogenetic tree reconstruction. The learning model is done

through the tutorial and discussion in the classroom / lab. In addition to self-

directed learning through tasks, learners are directed to cooperate in group

work. Assessment of learning outcomes is done through an evaluation board,

independent tasks, and the ability to write and present a given task.




computing sciences


Be able to formulate problems of bioinformatics in the form of a

computational model and solve it with the help of software.

Being able to choose an alternative solution sequence alignment

(sequence alignment)

Being able to apply the sequence alignment algorithms and structure of

the network to identify genetic mutations

SUBJECT

sequence Alignment

Protein folds

phylogenetic trees

PRECONDITION

-

REFERENCES

1. Isaev, Alexander, "Introduction to Mathematical Methods in

Bioinformatics", Springer-Verlag, 2004

2. Shen, Nankai Shiyi, "Theory and Mathematical Methods for

Bioinformatics", Springer-Verlag, 2008

LIBRARY SUPPORT

Ian Korf, Mark Yandell, Joseph Bedell, "Basic Local Alignment Search

Tools" Oreilly 2003

COURSES

Name Subjects : Mathematics of Derivatives

CS Code : KM185375

Credit : 3

Semester : 3

COURSE DESCRIPTION

This course provides mathematical models to solve practical problem in three

basic aspect of financial market : pricing the financial assets, pricing of

financial derivative products, and risk management. The discussions are

focused on arbitrage principles, stochastics models of stock and interest rate,

Ito’s lemma, modelling of financial derivative product, analytic and numerical

methods to solve the financial derivative differential equations. The solutions

are used to design the risk management of financial derivative investments.






computing sciences







Students are able to learn 3 basic aspects of financial market : price of

financial assets, financial derivative products, adn risk management.

Students are able to learn and use the basic principles of mathematical

models development of financial assets and the financial derivatives

products, i.e arbitrage principles.

Students are able to learn the development of mathematical models of

financial product and its derivatives and their solutions analytically and

numerically, and to provide the analysis.

Students are able to extend the mathematical model of financial product

and its derivatives analytically and numerically.

SUBJECT

Financial derivatives products

Stochastic and partial differential equations

Numerical solutions

PRECONDITION

1. Numerical methods

2. Statistical methods

3. Multivariable calculus

REFERENCES

1. Jiang, Lishang, Mathematical Modeling and Methods of Option Pricing,

World Scientific, 2005

2. Willmot, Paul, et al, The Mathematics of Financial Derivatives,

Cambridge Press, 1995

3. Higham, Desmond J, An Introduction to Financial Option Valuation:

Mathematics, Stochastics and Computation 1st Edition, Cmabridge

2004.

4. Hull, JC, Options, "Futures and Other Derivatives", Prentice Hall 2005

5. Seydel, Rüdiger, Tools for Computational Finance, Springer, 2002

LIBRARY SUPPORT

-

COURSES

Name Subjects : Risk Analysis

CS Code : KM185376

Credit : 3

Semester : 3

COURSE DESCRIPTION

This course provides the concepts and methodologies in risk analysis theory,

risk models with uncertainty to analyze risks, optimization concepts in risk

analysis. Subsequently, some the applications of optimization concepts in risk

analysis are presented in some areas such as insurance, project risks, and

product assesment.




computing sciences






PLO-5 Students are able to make use of the principles of long life learning

to improve knowledge and current issues on mathematics


1. Students are able to explain the concepts and methodologies in risk

analysis theories.

2. Students are able to use the risk models to analyze risk in insurance

and other fields.

3. Students are able to explain the concept of optimization in risk analysis

4. Students are able to apply the concept of optimization in risk analysis

for some fields such as insurance, project risk, and product assesment.

SUBJECT

Risk modelling: time series, Markov chain, birth and death model,

copula

Risk optimization

PRECONDITION

Probability theory

REFERENCES

1. Quantitative Risk Analysis, David Vose, Wiley, 2009

2. Probability and Risk Analysis, Igor Rychlik and Jesper Ryden,

Springer, 2006

LIBRARY SUPPORT

COURSES

Name Subjects : Graph Algebra

CS Code : KM185377

Credit : 3 credits

Semester : 3

COURSE DESCRIPTION




computing sciences


SUBJECT

Linear Algebra in Graf

Spectral Graph Theory

Graf Partitions

PRECONDITION

REFERENCES

LIBRARY SUPPORT

COURSES

Name Subjects : Theory of Computing

CS Code : KM185378

Credit : 3

Semester : 3

COURSE DESCRIPTION




computing sciences


SUBJECT

Automato

Language theory

complexity theory

PRECONDITION

REFERENCES

LIBRARY SUPPORT

COURSES

Name Subjects : Wavelets and Applications

CS Code : KM185379

Credit : 3

Semester : 3

COURSE DESCRIPTION




computing sciences


SUBJECT

multiresolution analysis

Orthogonal wavelet

filter Bank

PRECONDITION

REFERENCES

LIBRARY SUPPORT

COURSES

Name Subjects : Advanced Partial

Differential Equations

CS Code : KM185380

Credit : 2

Semester : 3

COURSE DESCRIPTION




computing sciences







SUBJECT

PDP Linear and Non-Linear

Variational methods

Free Boundary Value Problems

PRECONDITION

REFERENCES

LIBRARY SUPPORT

COURSES

Name Subjects : Inverse Problems

CS Code : KM185381

Credit : 2

Semester : 3

COURSE DESCRIPTION

In this course is studied about invers problem, some methods to solve inver

problem, regulation method and convergence of linear and non linear

regulation




computing sciences


The student able to understand about invers problem, can formulate the

problem and solve it.

The student able to analyze the convergence of regulation method,

apply to solve invers problem.

The student able to determine the exact method for invers problem.

SUBJECT

Linear Inverse problem

Linear Regulation Method

Convergence Analyze of Regulation Method

Non Linear Regulation Method

PRECONDITION

Functional analysis

REFERENCES

1. Isakov, V, 2006, Inverse Problems for Partial Differential Equations,

Springer Science Business Media, Inc.

2. Tarantola,A , 2008, Inverse Problem Theory and Methods for Model

Parameter Estimation, Library of Congress Cataloging-in-Publication

Data, SIAM

3. Kaipio, J dan Somersalo, E. 2005, Statistical and Computational

Inverse Problems, Springer Science Business Media, Inc.

4. Hohage, T., 2002, lecture notes on Inverse Problems, University of

G¨ottingen

LIBRARY SUPPORT

COURSES

Name Subjects : Fuzzy Systems

CS Code : KM185382

Credit : 2

Semester : 3

COURSE DESCRIPTION

This course aims to give basic concepts and to further increase the structure

of fuzzy theory and its application, this lecture consists of two parts: theory

and application part. The first part (part theory) covers the basic concepts and

operations of fuzzy sets, fuzzy set of multi-dimensional expansion of fuzzy

theory to the number and function, development properties and the probability

to fuzzy logic theory. The second part is an application that consists of a fuzzy

inference techniques, application of fuzzy logic inference, decision-making in

fuzzy environment




computing sciences


Being able to develop mathematical concepts, especially in the form of

fuzzy

Able to formulate a common problem in the form of fuzzy mathematics

models and get a settlement

Being able to apply the frame of mathematics and computational

principles to solve the problems of the development of intelligent

systems

Being able to identify problems and develop mathematical models and

analyze the relevant fuzzy behavior

Being able to communicate the results of research in a scientific forum

at the national or international level.

Able to develop contemporary science and technology by mastering and

understanding, approach, method, scientific principles along with their

application skills in the field of optimization of the system, or computer

science

SUBJECT

Fuzzy Set Theory

Fuzzy logic

fuzzy Decision

PRECONDITION

REFERENCES

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

Sets", Physica Heidelberg, 2001

2. Klir, GJ and B. Juan, "Fuzzy Sets and Fuzzy Logic", Prentice Hall, New

Jersey, 2001

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

Academic Publishers, 1996

4. Zadeh, LA., "Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected

Papers", Kluwer Academic Publishers, 1996

LIBRARY SUPPORT

COURSES

Name Subjects : Graf and Applications

CS Code : KM185383

Credit : 2

Semester : 3

COURSE DESCRIPTION




computing sciences


SUBJECT

Graph Theory

Application of graphs in Mechanical Problems

PRECONDITION

REFERENCES

LIBRARY SUPPORT

COURSES

Name Subjects : Topics of Applied Analysis

CS Code : KM185384

Credit : 2

Semester : 3

COURSE DESCRIPTION

On this subject, topic-topic presented the latest in the field of analysis,

algebra and its application study of paper and paper terkaitan presented the

topic for the next student in the form of presentation. From this study are

expected to emerge thesis topics




computing sciences


1. Students are able to assess the new topics of analysis, algebra and its

application

2. Students are able to assess the paper / paper relating on the topic

3. Students are able to present a role in the form of presentations and

writing

SUBJECT

The items you just about the analysis and its application

Recent Developments Analysis

PRECONDITION

-

REFERENCES

Text books and related Paper

LIBRARY SUPPORT

__

COURSES

Name Subjects : Topics of Computing

CS Code : KM185385

Credit : 2

Semester : 3

COURSE DESCRIPTION

On this subject, topic-topic presented the latest in the field of computer science

and computing. Study of paper and paper terkaitan presented the topic for the

next student in the form of presentation. From this study are expected to

emerge thesis topics




computing sciences


1. Students are able to assess the new topics of computer science and

computing



writing

SUBJECT

The items you new to computer science and computing

Recent Development of Computer Science and computing

PRECONDITION

-

REFERENCES


LIBRARY SUPPORT

__

COURSES

Name Subjects : Topics of Mathematical

Modeling

CS Code : KM185386

Credit : 2

Semester : 3

COURSE DESCRIPTION

On this subject, topic-topic presented the latest in the field of mathematical

modeling. Study of paper and paper terkaitan presented the topic for the next

student in the form of presentation. From this study are expected to emerge

thesis topics




computing sciences






PLO-5 Students are able to make use of the principles of long life

learning to improve knowledge and current issues on mathematics


1. Students are able to assess the new topics of mathematical modeling



writing

SUBJECT

1. Pemodelanan the items you just about math

2. Mathematical modeling Recent Developments

PRECONDITION

-

REFERENCES

Text books and papers related

LIBRARY SUPPORT

-

COURSES

Name Subjects : Topics of Applied Algebra

CS Code : KM185387

Credit : 2

Semester : 3

COURSE DESCRIPTION

Of this course-topic presented the latest topics in the field of algebra and its

application. Study of paper and paper terkaitan presented the topic for the

next student in the form of presentation. From this study are expected to

emerge thesis topics




computing sciences


1. Students are able to assess new topics algebra and its application

2. Students are able to assess the paper / papers relating about the topic

mentioned


writing

SUBJECT

The items you just about analysis, algebra and its application

Recent Developments Algebra

PRECONDITION

-

REFERENCES


LIBRARY SUPPORT

__

COURSES

Name Subjects : Topics of Optimization

CS Code : KM185388

Credit : 2

Semester : 3

COURSE DESCRIPTION

On this subject, topic-topic presented the latest in the field of optimization.

Study of paper and paper terkaitan presented the topic for the next student in

the form of presentation. From this study are expected to emerge thesis topics




computing sciences


1. Students are able to assess the new topics of optimization



writing

SUBJECT

1. The items you just about pemodelanan optimization

2. Recent Developments Optimization

PRECONDITION

-

REFERENCES

Text books and papers related

LIBRARY SUPPORT

-

Documents

SYLLABUS MASTER OF MATHEMATICS