5.6 Undergraduate Mathematics Study Program
5.6.9 Long-term Research Theme
5.6.10 List of Compulsory Subjects for Undergraduate Mathematics Study Program by Semester
SEMESTER I
CODE COURSE Credit PREREQUISITE
C Pr T
MAM61101 LOGIC AND SETS+ 3 - 3
MAM61102 ELEMENTARY LINEAR ALGEBRA 4 - 4 -
MAM61201 CALCULUS I+ 4 - 4 -
MAM61401 SCIENCES 2 - 2 -
MAM61001 ALGORITHM PROGRAMMING 2 1 3 - MAM61301 INTRODUCTION TO STATISTICS 2 1 3 -
TOTAL 19 -
SEMESTER II
CODE COURSE Credit
PREREQUISITE C Pr T
MAM62101 DISCRET MATHEMATICS 3 - 3 MAM61101
MAM62102 ALGEBRAIC STRUCTURES+ 3 - 3 MAM61101
MAM62201 CALCULUS II+ 4 - 4 MAM61201
MAM62202 GEOMETRY ANALYTIC+ 3 - 3 -
UBU60005 ENGLISH 2 - 2 -
MAM62301 BASIC PROGRAMMING 2 1 3 MAM61301
TOTAL
18
SEMESTER III
CODE COURSE Credit
PREREQUISITE C Pr T
MAM61103 ALGEBRAIC STRUCTURES II+ 3 - 3 MAM62102
MAM61202 CALCULUS III+ 4 - 4 MAM62201
MAM61203 INTRODCTION TO COMPLEX
FUNCTION I+ 2 - 2 -
MAM61302 ORDINARY DIFFERENTIAL
EQUATION+ 4 - 4 MAM61102,
MAM62201 MAM61402 INTRODUCTION TO PROBABILITY 3 - 3 MAM61401,
MAM62201
MPK60006 CITIZENSHIP 3 - 3 -
TOTAL
19
SEMESTER IV
CODE COURSE Credit
PREREQUISITE
C Pr T
MPK60001-5 RELIGION 3 - 3 -
MAM62203 INTRODUCTION TO COMPLEX
FUNCTION II+ 2 - 2 MAM61203
MAM62302 PARTIAL DIFFERENTIAL EQUATION + 3 - 3 MAM61302
MAM62303 NUMERICAL MATHEMATICS 3 1 4 MAM61102,
MAM61301 MAM62201
MAM62401 MATHEMATICAL STATISTICS 4 - 4 MAM61402
TOTAL 16
SEMESTER V
CODE COURSE Credit
PRASYARAT
C Pr T
MAM61204 INTRODUCTION TO REAL ANALYSIS I 4 - 4 MAM61202
MAM61403 OPERATION RESEARCH I + 3 - 3 MAM61102
MPK60007 INDONESIAN 3 - 3 -
MPK60008 PANCASILA 2 - 2 -
TOTAL 12
SEMESTER VI
CODE COURSE Credit
PRASYARAT
C Pr T
MAM62204 INTRODUCTION TO REAL ANALYSIS II 2 - 2 MAM61204
MAM62304 MATHEMATICAL MODELLING 4 - 4 MAM62302,
MAM61403
UBU60004 ENTREPRENEURSHIP 3 - 3 -
TOTAL 9
SEMESTER VII
CODE COURSE Credit PREREQUISITE
C Pr T
UBU60002 INTERNSHIP/COMMUNITY SERVICE 3 - 3 PASSED ≥ 90 credits MAM60001 RESEARCH METHODOLOGY AND
SCIENTIFIC WRITING IN MATHEMATICS
2 - 2 MPK60007
TOTAL 5
SEMESTER VIII
CODE COURSE Credit PREREQUISITE
C Pr T
UBU60001 FINAL PROJECT 6 - 6 PASSED ≥ 120
c r e d i t s
TOTAL 6
TOTAL NUMBER OF COMPULSORY COURSES : 33 COURSES TOTAL NUMBER OF COMPULSORY COURSE CREDITS : 104 credits
5.6.11 List of Courses for Odd and Even Semester of Undergraduate Mathematics Study Program ODD SEMESTER COURSES
NO CODE COURSE credit STA
TUS
PREREQUISITE C Pr
T
1. MAM61101 LOGIC AND SETS+ 3 - 3 W -
2. MAM61102 ELEMENTARY LINEAR ALGEBRA+ 4 - 4 W -
3. MAM61201 CALCULUS I+ 4 - 4 W -
4. MAM61001 SCIENCES 2 - 2 W -
5. MAM61301 ALGORITHM PROGRAMMING 2 1 3 W -
6. MAM61401 INTRODUCTION TO STATISCTICS 2 1 3 W -
7. MAM61103 ALGEBRAIC STRUCTURES+ 3 - 3 W MAM62102
8. MAM61202 CALCULUS III + 4 - 4 W MAM62201
9. MAM61203 INTRODUCTION TO COMPLEX FUNCTION +
2 - 2 W -
10. MAM61302 ORDINARY DIFFERENTIAL EQUATION + 4 - 4 W MAM61102, MAM62201 11. MAM61402 INTRODUCTION TO PROBABILITY+ 3 - 3 W MAM61401
,
MAM62201
12. MPK60006 CITIZENSHIP 3 - 3 W -
13. MAM61204 INTRODUCTION TO REAL ANALYSIS I 4 - 4 W MAM61202 14. MAM61403 OPERATION RESEARCH I + 3 - 3 W MAM61102
15. MPK60007 INDONESIAN 3 - 3 W -
16. MPK60008 PANCASILA 2 - 2 W -
17. MAM61104 GRAPH THEORY 2 - 2 P MAM62101
18. MAM61105 FINITE GROUP THEORY 2 - 2 P MAM62102
19. MAM61106 FUZZY GROUP THEORY 2 - 2 P MAM62102
20. MAM61002 INTRODUCTION TO CHEMISTRY 3 - 3 P -
21. MAM61003 INTRODUCTION TO BIOLOGY 3 - 3 P -
22. MAM61004 INTRODUCTION TO PHYSICS 3 - 3 P -
23. MAM61303 DIFFERENCE EQUATION 3 - 3 P MAM61102
MAM61201
24. MAM61304 DATABASE SYSTEM 2 1 3 P MAM61101
MAM62301 25. MAM61404 FINANCIAL MATHEMATICS I 2 - 2 P MAM61201 26. MAM61405 MATHEMATICS FOR ECONOMIC AND
BUSINESS
3 3 P MAM62201
27. MAM61107 INTRODUCTION TO MODULE THEORY 2 - 2 P MAM61103 28. MAM61205 INTORUDCTION TO DIFFERENTIAL
GEOMETRY
3 - 3 P MAM61102 MAM61202 MAM62302
NO CODE COURSE credit STA TUS
PREREQUISITE C Pr
T 29. MAM61206 INTRODUCTION TO FUNCTIONAL
ANALYSIS
3 - 3 P MAM61204 30. MAM61305 NUMERICAL OPTIMIZATION I 2 1 3 P MAM61202
MAM62303 31. MAM61306 INTRODUCTION TO DISCRETE
DYNAMICAL
2 - 2 P MAM61303 MAM61202 32. MAM61307 NUMERICAL METHODS FOR NUMERICAL
DIFFERENTIAL I
2 1 3 P MAM61302, MAM62303 33. MAM61308 INTRODUCTION TO WAVE MODELLING 2 - 2 P MAM62302
34. MAM61309 VARIATIONAL CALCULUS 2 - 2 P MAM62302
35. MAM61310 INTRODUCTION TO POPULATION DYNAMICS
2 - 2 P MAM62308 36. MAM61311 INTRODUCTION TO DIGITAL IMAGE
PROCESSING
2 1 3 P MAM62302, MAM62301
37. MAM61406 STOCHASTIC PROCESSES 3 - 3 P MAM62401
MAM61302 38. MAM61407 INSURANCE MATHEMATICS II 2 - 2 P MAM62403 39. MAM61408 INTRODUCTION TO RELIABILITY ANALYSIS 3 - 3 P MAM62401 40. MAM61207 INTRODUCTION TO FRACTAL GEOMETRY 2 1 3 P MAM61306
TOTAL CREDIT OF ODD SEMESTER COURSES 112
MATA KULIAH SEMESTER GENAP
NO CODE COURSE credit STA PREREQUISITE
C Pr T TUS
1. MAM62101 DISCRETE MATHEMATICS 3 - 3 W MAM61101
2. MAM62102 ALGEBRAIC STRUCTURES I + 3 - 3 W MAM61101
3. MAM62201 CALCULUS II + 4 - 4 W MAM61201
4. MAM62202 GEMOTRY ANALYTIC + 3 3 W -
5. UBU60005 ENGLISH 2 2 W -
6. MAM62301 BASIC PROGRAMMING 2 1 3 W MAM61301
7. MPK60001-5 RELIGION 3 - 3 W -
8. MAM62203 INTRODUCTION TO COMPLEX FUNCTION II + 2 - 2 W MAM61203 9. MAM62302 PARTIAL DIFFERENTIAL EQUATION + 3 - 3 W MAM61302 10. MAM62303 NUMERICAL MATHEMATICS 3 1 4 W MAM61102, MAM61301, MAM62201 11. MAM62401 MATHEMATICAL STATISTICS+ 4 - 4 W MAM61402 12. MAM62204 INTRODUCTION TO REAL ANALYSIS II 2 - 2 W MAM61204 13. MAM62304 MATHEMATICAL MODELLING 4 - 4 W MAM62302, MAM61403
14. UBU60004 ENTREPRENEURSHIP 3 - 3 W -
NO CODE COURSE credit STA PREREQUISITE C Pr T TUS
15. MAM62103 NUMBER THEORY 2 - 2 P MAM61101
16. MAM62104 LINEAR ALGEBRA 2 - 2 P MAM61102
17. MAM62105 APPLICATIONS OF ELEMENTARY LINEAR ALGEBRA
2 - 2 P MAM61102
18. MAM62305 SOFTWARE FOR MATHEMATICS 2 1 3 P MAM61301 19. MAM62402 INTRODUCTION TO LINEAR REGRESSION 2 - 2 P MAM61401 20. MAM62403 INTRODUCTION TO EXPERIMENTAL DESIGN 2 - 2 P MAM61401
21. MAM62106 COMBINATORICS 2 - 2 P MAM62101
22. MAM62107 MATRIX RING 2 - 2 P MAM61103
23. MAM62108 CODING THEORY 2 - 2 P MAM61102,
AM62101
24. MAM62205 UNIVALENT FUNCTION 2 - 2 P MAM61203
25. MAM62306 INTRODUCTION TO DATA MINING 2 1 3 P MAM61304
26. MAM62307 SPECIAL FUNCTION 2 - 2 P MAM61302
27. MAM62308 INTRODUCTION TO CONTINUOUS DYNAMICAL SYSTEM
2 - 2 P MAM61302 28. MAM62309 INTRODUCTION TO COMPUTATIONAL
INTELLIGENCE
2 1 3 P MAM62201, MAM62301 29. MAM62404 INSURANCE MATHEMATICS I 2 - 2 P MAM61402 30. MAM62405 INTRODUCTION TO FORECASTING METHOD 2 P MAM62402 31. MAM62406 FINANCIAL MATHEMATICS II 2 - 2 P MAM62201, MAM61302, MAM61404 32. MAM62206 INTRODUCTION TO TOPOLOGY 2 -
2
P MAM61204
33. MAM62207 MEASURE THEORY 2 -
2
P MAM61204 34. MAM62310 NUMERICAL METHODS FOR PARTIAL
DIFFRENTIAL EQUATIONS
2 1 3
P MAM61307 35. MAM62311 INTRODUCTION TO FINITE ELEMENT
METHODS
2 1 3
P MAM62302, MAM61307 36. MAM62312 INTRODUCTION TO OPTIMAL CONTROL 2 - 2 P MAM61302 37. MAM62313 NUMERICAL OPTIMIZATION II 2 1 3 P MAM61305
38. MAM62407 INSURANCE RISK MODEL 3 - 3 P MAM62401
39. MAM62408 GAME THEORY 2 - 2 P MAM61403
40. MAM62409 OPERATION RESEARCH II+ 3 - 3 P MAM61403
TOTAL CREDIT OF EVEN SEMESTER COURSES 103
Algebra KBI : 1
Analysis KBI : 2
COURSES ON ODD/EVEN SEMESTER
NO CODE COURSE Credit STA
TUS PREREQUISTE C Pr T
1. MAM4900 RESEARCH METHODOLOGY AND SCIENTIFIC WRITING IN MATHEMATICS
2 - 2 W* MPK60007
2. UBU60002 INTERNSHIP/COMMUNITY
SERVICE 3 - 3 W PASSED ≥ 90
credits
3. UBU60001 FINAL PROJECT 6 - 6 W PASSED ≥ 120
credits 4. MAM60101 CAPITA SELECTA IN ALGEBRA 2 - 2 P MAM61103 5. MAM60201 CAPITA SELECTA IN ANALYSIS 2 - 2 P MAM61204 6. MAM60301 CAPITA SELECTA IN APPLIED
ANALYSIS 2 - 2 P MAM62302,
MAM62308 7. MAM60302 CAPITA SELECTA IN SCIENTIFIC
COMPUTING 2 - 2 P MAM61307
8. MAM60303 CAPITA SELECTA IN COMPUTER
VISION 2 - 2 P MAM62309,
MAM61311 9. MAM60401 CAPITA SELECTA IN OPERATION
RESEARCH 2 - 2 P MAM61403
10. MAM60402 CAPITA SELECTA IN PROBABILITY
AND STTOCHASTIC PROCESSES 2 - 2 P MAM62401 TOTAL CREDIT OF ODD/EVEN SEMESTER COURSES 25
Description:
W : COMPULSORY course P : SELECTED course K : COURSE
Pr : Practice
+ : Course with FEEDBACK
* : Courses offered in odd or even semesters
“MAM6abcd” code notes:
MAM : Mathematics of mathematics and natural science 6 : Undergraduate Program (S1)
a : semester, that is 1: odd, 2: even, and 0: odd/even semester
b : Mathematics KBI, namely
Applied Analysis and Computational KBI Science
: 3 Industrial and Financial Mathematics KBI : 4 cd : course sequence number
5.6.12 Syllabus for Undergraduate Mathematics Study Program Course 1. ALGEBRA KBI COURSE
MAM61101 LOGIC AND SETS 3 credits Prerequisite:-
Description
In this course, logic is focused on how to construct and prove theorems, lemmas, propositions, and other properties. Then discuss the basic concepts of sets from a theoretical side, so, some simple properties are proven logically and systematically.
Course Learning Outcome
After taking this course, students are able to compile mathematical statements with mathematical logic symbols, both in the form of sets, relations, and functions.
Material
Presumption: Negation, Conjunction, Disjunction, implication, biimplication, tautology and contradiction, conversion, contraposition, inverse, logical laws, inference rules, mode ponent, modus tolens, universal quantor, existential quantor, method of proof, set and operation, law -Laws on sets, proving sentence sets, relations and functions, Cartesian product, equivalence relations, injective, surjective and wise functions.
References:
1. Soehakso, R.M.J.T., 1985, Pengantar Matematika Modern, FMIPA-UGM.
2. Torski, A., 1990, Introduction to Logic, Oxford-Press.
MAM4521 ELEMENTARY LINEAR ALGEBRA 4 credits Prerequisite: -
Description
This lecture discusses the relationship between matrices, systems of linear equations, and linear transformations. In addition, students are also introduced to the concept of vector space as an abstraction from a set of vectors known in physics. Theorem proof is introduced, but students are not required to master the proof.
Course Learning Outcome
After taking this course, students can explain the relationship between matrices, systems of linear equations, and linear transformations and can explain basic concepts and properties related to vector spaces.
Material
Matrixes: types of matrixes, operations on matrixes, elementary transformations, inverse matrices, determinants: calculating the determinant value, determinant properties, Linear Equation Systems, Vectors in R2 and R3: vector algebra, point product, cross product, Vector Space Euclidean: space of n Euclidean dimension, General Vector Space: Real vector space, subspace, linear freedom, base, dimension, row space, column space, Null space, rank, nullity, Inner Product Space: inner product, angle and orthogonality, orthogonal basis, Gram- Schmidt process, change of base, Eigenvalues and Eigenvectors, orthogonal diagonalization, linear transformation from Rn to Rm, properties of linear transformation, similarity.
References
1. Anton, H., Rorres, C, 2004, Aljabar Linier Elementer ( versi aplikasi), Jilid 1, Erlangga, Jakarta.
2. Hoffman dan Kunze, 1984, Linier Algebra, Prentice-Hall.
MAM62101 DISCRETE MATHEMATICS 3 credits Prerequisite: MAM61101 LOGIC AND SETS
Description
Material discussion in this course is in terms of theory and application. Several properties regarding discrete concepts are attested and interpreted in application examples.
Course Learning Outcome
After taking this course, students can explain the basics of proof, combinatorics and the relationship between discrete mathematical concepts and programming.
Material
Proving strategy (direct and indirect), principle of mathematical induction, basics of counting (addition and multiplication rules, the inclusion-exclusion principle), permutations and combinations, binomial and multinomial coefficients, pigeonhole principle: simple and strong form, and Ramsey's theorem, binary relations: representations and properties, ordered sets (poset), lattice, Boolean algebra: simplification of Boole expressions, SOP, POS, Karnough maps, and the Quine-McCluskey algorithm.
References
1. Rosen, H.K., 1999. Discrete Mathematics and Its Applications. Singapore: McGraw-Hill.
2. Grimaldi, R.P., 1994, Discrete and Combinatorial Mathematics: An Applied Introduction, 3rd Edition, Addison-Wesley Publishing, New York.
3. Dierker, P.F., and Voxman, W.L., 1986, Discrete Mathematics, Harcaurt Brace Javanovich Inc, New York.
MAM62201 ALGEBRA STRUCTURE I 3 credits Prerequisite: MAM61101 LOGIC AND SETS
Description
In this lecture, we discuss about structures that involve a set with one binary operation. The basic concepts that must be mastered by students are identification of set members and binary operations. The emphasis of learning in this course is understanding the definitions related to groups, as well as proving the theorems, lemmas, etc., and trying to get illustrations in real problems, so that students understand the concept more easily.
Course Learning Outcome
After taking this course, students can master basic concepts about groups, and prove the properties, theorems, and lemmas associated with groups.
Material
Binary operations, algebraic structure, groups and properties, group order, group element order, complex and subgroup, properties of subgroups, cyclic groups, properties and classification of cyclic groups, left coset, right coset, Lagrange's Theorem, index, normal
subgroup and factor group, homomorphism, isomorphism, homomorphism Fundamental Theorem.
References
1. Andari, A. , 2015, Teori Grup, UB Press, Malang.
2. Bhattacharya, P.BB, S.K. Jain, dan S.R. Nagpaul., 1994, Basic Abstract Algebra, Cambrige University Press, New York.
3. Chaudhuri, N.P. 1983. Abstract Algebra. Tata McGraw- Hill Publishing Company Limite New Delhi
4. Dummit, D.S. dan R.M.Foote.,2002, Abstract Algebra, Incorporation, New York. Ed.
John Wiley and Sons
5. Durbin, J.R., 1979, Modern Algebra, John Willey & Sons, Inc, New York.
6. Herstein, I.N., 1986, Abstract Algebra, Mac Millan Publishing Company, New York.
7. Freleigh, J.B. ,1970, A First Course in Abstract Algebra, John Willey & Sons.
8. Lang, 1995, Algebra, Addison-Wesley Publishing Company New York;
9. Raisinghania, Aggarwal, 1980, Modern Algebra, S. Chand & Company Ltd., New Delhi
MAM4524 ALGEBRA STRUCTURE II 3 credits Prerequisite: MAM 4512 ALGEBRA STRUCTURE I
Description
In this lecture, a structure that involves a set with two binary operations is discussed, hereinafter referred to as the ring, field and integral area, which is an extension of the group concept. The emphasis of learning in this course is understanding the definitions related to ring, field and integral areas, alongside their properties, as well as proving the theorems, lemmas, etc., and trying to illustrate real problems, so that students understand the concept more easily.
Course Learning Outcome
After taking this course, students can prove the theorems and properties of ring theory.
Material
Ring, field, integral area, subring and ideal, ideal and ideal principal properties, ring characteristics, congruence, kl; residual as-class, factor field of integral region, ring polynomial, factorization of polynomials over field, division algorithm, ring homomorphism , ring factor, homomorphism fundamental theorem, ideal prime, maximum ideal, principal ideal ring, Euclid ring, single factorization area.
Refrences
1. Andari, A,. 2014. Ring, Field dan Daerah Integral, UB Press, Malang.
2. Bhattacharya, P.BB, S.K. Jain, dan S.R.Nagpaul. 1994. Basic Abstract Algebra. Cambrige University Press. New York.
3. Chaudhuri,N.P. 1983. Abstract Algebra. Tata McGraw- Hill Publishing Company Limited.
New Delhi.
4. Dummit, D.S. dan R.M.Foote. 2002. Abstract Algebra, 2nd Ed. John Wiley and Sons Incorporation. New York.
5. Durbin, J.R. 1979. Modern Algebra, John Willey & Sons, Inc, New York;
6. Herstein, I.N. 1986. Abstract Algebra, Mac Millan Publishing Company, New York;
7. Freleigh, J.B. 1970. A First Course in Abstract Algebra, John Willey & Sons.
8. Lang, 1995, Algebra, Addison-Wesley Publishing Company New York;
9. Raisinghania, Aggarwal, 1980, Modern Algebra, S. Chand & Company Ltd., New Delhi.
MAM62103 NUMBER THEORY 2 credits Prerequisite: MAM61101 LOGIC AND SETS
Description
In this lecture, the definition of numbers is introduced in axiomatic way, so that students' understanding of the definitions and theorems / properties of numbers is needed.
Course Learning Outcome
After taking this course, students can explain number theory axiomatically.
Material
Natural numbers and their operations on sets, number symbols, axiomatic number theory, Peano's axioms, integers: division, modulo arithmetic, Diophantine equations; properties of prime numbers, rational numbers: their sequence and operation; rational number system as an extension of natural numbers, real numbers, algebraic properties of real numbers.
References:
1. Wirasto, R.M. 1971, Pengantar Ilmu Bilangan, F-MIPA-UGM.
2. Sukirman,M.P.1986, Ilmu Bilangan, Karunia, Jakarta.
3. Niven, I dan Friens,1991, An Introduction to The Theory of Numbers, John Wiley & So.
MAM62104 ALINEAR ALGEBRA 2 credits Prerequisite: MAM61102 ELEMENTARY LINEAR ALGEBRA
Description
This lecture discusses the deepening of elementary linear algebra, with a focus on proving several theorems, lemmas and properties.
Course Learning Outcome
After taking this course, students can prove theorems, lemmas, and other properties of the concept of vector space and linear transformations.
Material
Theory about: vector space over the field (field), subspace, linear freedom, bases and dimensions, rank and nullity, eigenvalues and eigenvectors, diagonalization, linear transformations, kernels and ranges, inverse linear transformations, generators, subspaces, vectors - linear and non-linear independent vectors, Linear transformations from Rn to Rm, Similarities.
References
1. Lang, S; 1972; Linear Algebra, Addison – Wesley Publishing Company; London.
2. Lang, 1995, Algebra, Addison-Wesley Publishing Company New York
MAM62105 APPLICATIONS OF ELEMENTARY LINEAR ALGEBRA 2 credits Prerequisite: MAM61102 ELEMENTARY LINEAR ALGEBRA
Description
This lecture discusses the application of Elementary Linear Algebra.
Course Learning Outcome
After taking this course, students have broader insights in the field of algebra, especially regarding the application of algebra.
Material
Forming Curves and Surfaces, Linear Geometric Programming and Cubic-splint Interpolation, Game Strategies and Leontive Economic Models, Cryptography, Assignment Problems, Graph Theory, Forest Management, Genetics, Age-Specific Population Growth, Harvesting Animal Populations, Least Square Method.
References
Anton, H., Rorres, C, 2005, Aljabar Linier Elementer (versi aplikasi), Jilid 2, Erlangga, Jakarta.
MAM61104 GRAPH THEORY 2 credits Prerequisite: MAM62101 DISCRETE MATHEMATICS
Description
This lecture discusses meaning of graphs and subgraphs, connected graphs, matrixes on graphs, Eulerian and bipartite graphs, Trees and spanning trees, planar graphs, graph coloring, chromatic polynomials, matching, dominant and independent sets, directed graphs, directed graph types, tournaments and matrixes on directed graphs.
Course Learning Outcome
After studying this course students can (1) understand the meaning of graphs and subgraphs, connected graphs, matrixes on graphs, Eulerian and bipartite graphs, Trees and spanning trees, planar graphs, graph coloring, chromatic polynomials, matching, dominant and independent sets, directed graphs, directed graph types, tournaments and matrices on directed graphs, (2) using the concept of re-expressing or communicating reading content or ideas related to the field of mathematics both in writing and orally.
Material
Understanding graphs and subgraphs, connected graphs, matrices on graphs, Euler graphs and bipartite graphs, Trees and spanning trees, planar graphs, graph coloring, chromatic polynomials, matching, dominant and independent sets, directed graphs, directed graph types, tournaments and matrixes on directed graph.
References
1. Marsudi., 2015, Teori Graf, Buku Ajar FMIPA Universitas Brawijaya
2. Vasudev, C., 2006, Graph Theory with Applications, New Age International (P) Ltd., Publishers, New Delhi.
3. Narsingh, D., 1994, Graph Theory with Applications to Engineering and Computer Science, Prentice Hall, New Delhi.
4. Bondy, J.A. and Murty, USR., 1976, Graph Theory withApplications, Elsevier Science, New York.
MAM61105 FINITE GROUP THEORY 2 credits Prerequisite: MAM62102 ALGEBRA STRUCTURE I
Description
In this lecture, groups with finite order are discussed, which is one type of group. The emphasis of this course is on proving theorems, lemma, etc, and trying to obtain an illustration in real problems.
Course Learning Outcome
After taking this course, students can interpret Sylow's theorem.
Material
Cycle, permutation group, symmetry group, permutation class, normalizer, centralizer, flashlight, subgroup commutator, group action on set, Sylow's theorem.
References
1. Ledermann, W., 1984, Introduction to the Theory of Finite Group, Interscience Publisher, Inc.
2. Fraleigh, J.B., A First Course in Abstract Algebra, 1989, Fourth Edition; Addison- Wesley Publishing Company. Inc.
3. Kurosh, A.G, 1960, the Theory of Groups, Chelsea Publishing Company, New York.
MAM61106 FUZZY GROUP THEORY 2 credits Prerequisite: MAM62102 ALGEBRA STRUCTURE I
Description -
Course Learning Outcome
After taking this course, students prove the characteristics of fuzzy groups.
Material
Fuzzy set, fuzzy subgroup, normal fuzzy subgroup, homomorphism and isomorphism, relative fuzzy order, fuzzy order in cyclic group, properties of fuzzy normal subgroup, fuzzy subgroup characteristics, Abelian fuzzy subgroups, Cayley fuzzy theorem, Lagrange fuzzy theorem, fuzzy nilpotent subgroups.
References
1. Kandasamy, W.B.V., 2003, Smarandache Fuzzy Algebra, Department of Mathematics Indian Institute of Technology Madras.
2. Mordeson, J.N., Bhutani, K.R., Rosenfeld A., 2005, Fuzzy Group Theory, Springer-Verlag Berlin Heidelberg.
3. Rosenfeld, A., 1971, Fuzzy Groups, Journal of Mathematical Analysis and Applications, 35, 512 – 517
4. Setiadji, 2009, Himpunan dan Logika Samar, Graha Ilmu, Yogyakarta.
5. Zadeh, L.A.,1965, Fuzzy Sets, Information and Control, 8, 1965, 338 – 353
107
MAM62106 COMBINATORICS 2 credits Prerequisite: MAM62101 DISCRETE MATHEMATICS
Description
This lecture discusses multisets, permutations and combinations in multisets, the principle of inclusion-exclusion and its application, recurrence relation and generator function, Catalan numbers, Stirling and Bell, combinatorial design.
Course Learning Outcome
After taking this course, students can explain about Multiset, Permutation and combination, the principles of Inclusion - Exclusion, Catalan Numbers, Latin squares, semilatin rectangles, Block design (BBD and BIBD) and the Steins Triple system (STS).
Material
Multiset, Permutation and combination on multisets, Inclusion Principles - Exclusion, Stirling and Bell, Catalan Numbers, Homogeneous and non-homogeneous recurrence relations solutions with generating functions, Introduction to modular arithmetic, Latin squares, semilatin squares, Block design (BBD and BIBD), Steins Triple system (STS), Complete Marriage.
References:
1. Brualdi, R.A., 2004, Introductory Combinatorics, Pearson-Prentice Hall. New Delhi 2. Chuan-Chong, C. And Khee-Meng, K. 1992, Principles and Techniques in Combinatorics,
Singapore: World Scientific Publishing Co. Pte. Ltd.
MAM62107 MATRIX RING 2 credits Prerequisite: MAM61103 ALGEBRA STRUCTURE II
Description
This lecture discusses about the properties of a matrix with entries over the commutative ring.
Course Learning Outcome
After taking this course, students can:
1. Comparing the concept of a real number ring matrix with a commutative ring matrix 2. Determine the ideal and rank of a matrix on the commutative ring
3. Determine the solution of linear equation
4. Give examples of prime minima and radicals of commutative ring top matrix 5. Interpret Cayley Hamilton's theorem
6. Determine the results and zero divisor of matrix over the commutative ring.
Material
Commutative ring top module, matrix with entry over commutative ring, ideal, rank, linear equation, minimal prime and radical of ideal, Cayley Hamilton theorem, resultant, zero divider.
References
1. Brown, W.C., 1993, Matrices over Commutatif rings, Marcell Dekker, Inc. New York.
2. Strang, G., 1988, Linear Algebra and Its Application.
3. Hartley,B. dan Hawkes, T.O.,1970, Ring,Modules and Linear Algebra, Chapman and Hall LTD, London.
4. MacLane, S., Birkhoff, G. 1979, Algebra, Secon Edition, Macmillan Publishing Co., Inc., New York.
MAM62108 CODING THEORY 2 credits Prerequisite: MAM61102 ELEMENTARY LINEAR ALGEBRA,
MAM62101 DISCRETE MATHEMATICS
Description
In this lecture, it is discussed about the role of coding theory in a communication system, the structure of a linear code, and how to construct a good linear code. Basic knowledge in Elementary Linear Algebra and Discrete Mathematics II is required in this course.
Course Learning Outcome
After taking this course, students can master the basic concepts of Coding Theory which provide an important description of application aspects from several subjects in mathematics such as Elementary Linear Algebra, Structural Algebra, and Combinatorics in the world of Computer Science.
Material
Communication channels, Hamming distance and weight, binary code, error-correcting codes, decoding, sphere-packing bound, binary linear code, dual code, linear code on finite fields, generator and parity check matrices, linear code equivalents, multiple linear code constructs: Hamming code, Golay, Hadamard, Reed-Muller, BCH, cyclic code.
References
1. Bierbrauer, Juergen, 2005, Introduction to Coding Theory, Chapman & Hall/CRC.
2. Ling, San dan Xing, Chaoping, 2004, Coding Theory: A First Course, Cambridge University Press.
3. Garrett, Paul, 2004, The Mathematics of Coding Theory, Pearson Prentice Hall.
MAM61107 INTRODUCTION TO MODULE THEORY 2 credits Prerequisite: MAM61103 ALGEBRA STRUCTURE II
Description
This lecture discusses development of group and ring. A structure involving two sets with two binary operations, hereinafter referred to as a module over the ring. The emphasis of learning in this course is understanding the definitions related to the module on the ring, along with its properties, as well as proving the theorems, lemmas, etc, and trying to obtain illustrations in real problems, so, the students understand the concept more easily.
Course Learning Outcome
After taking this course, students can explain and can prove the properties, theorems, and lemmas associated with the module.