1. Laurene Fauset, “Fundamental of Artificial Neural Networks”, Penerbit Prentice Pagel, 1994 2. Simon Haykin, “Kalman Filtering and Neuralnetwork”, Penerbit John Wiley & Sons, 2001 3. James A. Freeman and David M. Skapura, “Neural Networks Algorithms, Applications, and
Programming Techniques”, Penerbit Addison Wesley, 1991
‐ Quiz II network support backprropagation (14, 15) students are able to read
scientific papers that apply neural networks to solve problems
‐ Assessing international journals or proceedings
Presentation 2x (2x50 ") ‐ Summary results of the study
‐ Writing about some of the problems given solutions
The accuracy describes
understanding and solving cases
20%
16 FINAL EXAM
Course
Course Name : Artificial Neural Network
Course Code : KM184828
Credit : 2
Semester : 8
Description of Course
The course of artificial neural networks is a course that studies computational algorithms that mimic how biological neural networks work. This course is part of the Data Science, because the algorithm learned works well when applying data processing.
Learning Outcome
[C4]
Able to illustrate the framework of mathematical thinking in particular areas such as analysis, algebra, modeling, system optimization and computing science to solve real problems, mainly in the areas of environment, marine, energy and information technology.
[C5] Able to explain ideas and knowledge in mathematics and other fields to the society, in similar professional organizations or others.
[C5] Able to choose decisions and alternative solutions using data and information analysis based on an attitude of leadership, creativity and have high integrity in completing work individually or in a team.
Course Learning Outcome
1. Students are able to explain in any field the application of ANN
2. Students are able to analyze the simplest ANN algorithm to recognize AND, OR, NAND and NOR logic patterns.
3. Students are able to well explain the different implementation of ANN algorithm with 1 processing element and multi processing element.
4. Students are able to properly explain the network capable of storing memory
5. Students are able to properly explain the basic concepts of competition-based networks and problems that the network can solve
6. Students are able to explain the difference between the concept of backpropagation and varietin network algorithms
7. Students are able to properly examine the scientific work on the ANN application
Main Subject
1. Modeling of artificial neural networks from biological neural networks, 2. A simple pattern recognition with Perceptron, Hebb and Adaline, 3. Character recognition with Percepron, Associative memories, 4. Classification with BP, and LVQ,
5. Clustering with Kohonen SOM, 6. Forecasting BP, and RBF 7. Alternative model of ANN
Prerequisites
Linear Algebra Elementer Computer Programming Reference
1. Irawan, M. Isa, “Dasar-Dasar Jaringan Syaraf Tiruan ”, Penerbit ITS Press, 2013
Supporting Reference
1. Laurene Fauset, “Fundamental of Artificial Neural Networks”, Penerbit Prentice Hall, 1994
2. James A. Freeman and David M. Skapura, “Neural Networks Algorithms, Applications, and Programming Techniques”, Penerbit Addison Wesley, 1991
3. Simon Haykin, “Kalman Filtering and Neuralnetwork”, Penerbit John Wiley & Sons, 2001
Study Program Name Bachelor, Mathematics Department, FMKSD-ITS Course Name Elementary Linear Algebra
Course Code KM184203
Semester 2
Sks 4
Supporting Lecturer Dian Winda S, SSi, MSi
Materials • Matrices and Vectors
• Vector Space
• Linear Transformation Learning
Outcome [C2] Able to explain basic concepts of mathematics that includes the concept of a proof construction both logically and analytically, modeling and solving the simple problems, as well as the basic of computing.
[C3] Able to solve problems based on theoretical concepts in at least one field of mathematics:
analysis and algebra, modeling and system optimization, and computing science.
COURSE LEARNING OUTCOME
1. Students are able to follow developments and apply mathematics and be able to communicate actively and correctly either oral or written.
2. Students are able to explain intelligently and creatively about the significant role of ALE applications in the field of related knowledge clusters and other fields.
3. Students have a special ability and able to process their ideas enough to support the next study in accordance with the related field.
4. Students are able to present their knowledge in Elementary Linear Algebra independently or in teamwork.
Meets Sub Course Learning
Outcome Breadth of Materials Learning Methods Time
Estimatio n
Student Learning Experiences
Assessment Criteria
and Indicator Weight ing Assess
ment (%) 1-4 • Students are able to
complete the SPL by the Gaussian or Gauss Jordan elimination method And able to explain why SPL has no settlement.
• Students are able to use operations on the matrix and understand the algebraic properties of the matrix
• The understanding of system of linear equation and
augmented matrix
• Elementary Row Operation
• Gaussian and Gauss Jordan elimination
• Operation Matrix.
the properties of algebra in the matrix
[Ref. 1 page: 9-98]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion,
4x(2x50’)
Task Exercise
questions • Accuracy defines system of linear equation and augmented matrix.
• Ability to solve system of linear equation by elementary row operation
• Be able to solve using Gaussian and Gauss Jordan
• Be able to explain the properties of algebra in the matrix
15%
5-6 • Students are able to find inverse matrix, can complete system of linear equation by inversing matrix
• Students recognize the types of matrices and properties of the matrix
• Looking for Inverse matrix
• Complete the system of linear equation with the inverse matrix
• Matrix type: Diagonal matrix, triangular matrix, symmetry matrix and its properties [Ref. 1 page: 99-139]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) Task Exercise
questions • Be able to get the inverse of a matrix
• Able to complete system of linear equation by inversing matrix
• Be able to explain the types and properties of the matrix
5%
7-8 • Students are able to find the determinant of a matrix with Cofactor expansion
• Students are able to find the determinant of a matrix by Row Reduction
• Students are able to understand the properties of the determinant
• Counting determinants with Cofactor expansion
• Counting determinants by Reducing Rows
• the properties of the determinant
• complete SPL with Cramer rules [Ref. 1 page: 173-211]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) Task Exercise
questions • Able to calculate determinants with Cofactor expansion
• Capable of Counting determinants by Row Reduction
• Be able to explain the properties of the determinant
10%
• Students are able to complete the system of linear equation with the Cramer's rules
• Able to complete SPL with Cramer rules
9-12 Students are able to understand the vectors in space 2, space 3 and space n and operation on the vector
Students are able to define norm, product of point (product dot), distance, cross product, orthogonal set at R ^ n, seta geometry from linear System
vector in space 2, space 3 and space n
operation on the vector norm, dot product, distance, cross product, orthogonal set at R ^ n, set geometry of linear system [Ref. 1 page: 226-320]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) Task Exercise
questions Able to explain vectors in space 2, space 3 and space n
Be able to explain the operation on the vector
Ability to explain and norm, product of point (product dot), distance, cross product, orthogonal set at 𝑅 , seta geometry of linear System equation
15%
13,14 • Students are able to understand real vector spaces
• Students are able to understand the real vector subspace
• Students are able to understand linear and linearly independent combinations
• real vector space
• real vector subspace
• linear and linearly independent combinations
[Ref. 1 page: 328-375]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) TaSks Exercise
questions • Be able to explain real vector spaces and real vector subspaces
• Be able to explain linear combinations and linearly independent sets
5%
15,16 Midterm Exam
17-19 • Students are able to understand the basis and dimension of a vector space
• Students are able to determine the relative
• Base
• The vector space dimension
• Relative Coordinates
• Transition Matrix
• Classroom, Column Room, Empty Room
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) Tasks Exercise
questions • able to explain the basis and dimension of a vector space
• able to determine the relative coordinates of
15%
coordinates of a vector on a basis in a vector space
• Students are able to understand the row space, column space, blank space, rank, nullity of a matrix
• Rank and nullity
[Ref. 1 page: 377-455] a vector to a basis in a
vector space
• able to explain the row space, column space, empty space, rank, nullity of a matrix 20-22 Students are able to
understand the transformation of matrices from 𝑅 to 𝑅
Students are able to understand composition in matrix transformation
Definition of matrix transformation from R ^ n to R ^ m and its types
How to get the Matrix Transformation
Composition on the transformation matrix
[Ref. 1 thing: 456-515]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) Tasks Exercise
questions The student is able to explain the matrix
transformation from 𝑅 to 𝑅
Students are able to explain
Composition on matrix
transformation
10%
23-25 • Students are able to determine the eigenvalues and eigenvectors of a square matrix
• Students are able to determine the requirements of the matrix to be diagonalizable and can diagonalize the matrix
Eigenvalues
Eigenvector
Diagonalization of matrix 𝐴 with invertible matrix 𝑃 so that 𝐷 𝑃 𝐴𝑃
[Ref. 1 page: 539-569]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) Tasks Exercise
questions • able to determine eigenvalues and eigenvectors of a square matrix
• able to determine the requirement of the matrix to be
diagonalizable and can diagonalize the matrix
10%
26-30 • Students are able to understand inner product results in real vector spaces
• Students are able to understand the set of orthogonol in the inner product space
• Students are able to form an orthonormal basis by performing the Gram-Schmidt process
• Understanding Inside Outcomes
• the orthogonal set
• Gram-Schmidt process [Ref. 1 page: 608-660]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
4x(2x50’) Tasks Exercise
questions • able to explain inner product in real vector space
• Students are able to explain the set of orthogonol in the inner product space
• able to form an orthonormal basis by performing the Gram-Schmidt process
15%
Reference Main :
1. Howard Anton and Chris Rorrers, ”Elementary Linear Algebra, Tenth Edition", John Wiley and Sons, (2010).
Supporting :
1. C.D. Meyer,”Matrix Analysis and Applied Linear Algebra”, SIAM, (2000)
2. Steven J. Leon, "Linear Algebra with Applications", Seventh Edition, Pearson Prentice Pagel, (2006).
3. Stephen Andrilli and David Hecker,”Elementary Linear Algebra, Fourth Edition”, Elsevier, (2010) 4. Subiono., ”Ajabar Linear”, Jurusan Matematika FMIPA-ITS, 2016.
31-32 FINAL EXAM
STUDENT LEARNING EVALUATION PLAN
Courrse : Elementary Linear Algebra, Code: KM184203, sks: 4 sks, smt: 2 Learning Outcome:
1. Able to interpret basic mathematical concepts and compile evidence directly, indirectly, or with mathematical induction.
2. Able to identify simple problems, form mathematical models and solve them.
3. Mastering standard methods in the field of mathematics
4. Able to master the fundamental theory of mathematics which includes the concepts of set, function, differential, integral, space and mathematical structure.
5. Able to analyze the system and optimize its performance
6. Able to understand mathematical problems, analyze and solve them.
7. Able to observe, recognize, formulate and solve problems through mathematical approaches
Mee ts
Spesific Learning Objective (Sub‐Competence)
Elements of Competency in Assessment Number of questio
ns
Form of
Assessment %
Cognitive Psychomotor Affective
C1 C2 C3 C4 C5 C6 C7 P1 P2 P3 P4 P5 A1 A2 A3 A4 A5 1-4 • Students are able to complete SPL with the
Gaussian or Gauss Jordan elimination method As well as being able to explain why the SPL has no solution.
• Students are able to use operations on the matrix and understand the properties of algebraic spheres on the matrix
√ √
3 Task Training
Questions 15%
5-6 • Students are able to find matrix inverses, can solve SPL with matrix inverses
Students recognize the types of matrices and the properties of the matrix
√
√ 1 Task Training
Questions 5%
7-8 • Students are able to find the determinant of a matrix with Cofactor expansion
• Students are able to find the determinant of a matrix with Line Reduction
• Students are able to understand the properties of determinants
• Students are able to complete SPL with the rules of cramer
√
√ √ √
2 Task Training
Questions 10%
9-12 Students are able to understand vectors in space 2, space 3 and space n and operations in vectors
Students are able to determine norms, point products (dot products), distances, cross times (cross products), orthogonal sets at R ^ n, after geometry of linear systems
√
√
3 Task Training
Questions 15%
13,14 • Students are able to understand real vector space
• Students are able to determine sub real vector spaces
Students are able to determine linear combinations and linear free sets
√
√
1 Task Training
Questions
5%
15,16 ETS
17-19 • Students are able to determine the basis and dimensions of a vector space
• Students are able to determine the relative coordinates of a vector against a base in a vector space
Students are able to determine row space, column space, empty space, rank, the nullity of a matrix
√ √ √
3 Task Training
Questions 15%
20-22 Students are able to determine the
transformation of the matrix from 𝑅 to 𝑅 Students are able to determine composition in matrix transformation
√
√
2 Task Training
Questions
10%
23-25 • Students are able to determine the eigenvalues and eigenvectors of a square matrix
• Students are able to determine the
requirements for the matrix to be diagonalized and can diagonalize the matrix
√ √
2 Task Training
Questions 10%
26-30 • Students are able to understand the results of deep times in real vector space
• Students are able to understand the orthogonol set in the inner product space Students are able to form orthonormal bases by carrying out the gram-schmidt process
√ √
√
3 Task Training
Questions 15%
31, 32 EAS
Number
Questions 20
Percentage 100%
Information :
C1 : Knowledge P1 : Imitation A1 : Receiving
C2 : Comprehension P2 : Manipulation A2 : Responding
C3 : Application P3 : Precision A3 : Valuing
C4 : Analysis P4 : Articulation A4 : Organization
C5 : Syntesis & Evaluation P5 : Naturalisation A5 : Characterization C6 : Creative
Assessment Criteria
1. Task (20%)
After each chapter is taught the problem training is given 2. Quiz I (15%)
Quiz I was held at the 4th week, the material from the beginning to the 4th week material with 5 questions with the same weight value 3. ETS (25%)
ETS was held on the 8th week of the material from the beginning to the 7th week's material 4. Quiz II (15%)
Quiz II was held at the 12th week, the material from after ETS reached the 12th week material with 5 questions with the same weight value 5. EAS (25%)
EAS was held at the 16th week of material after ETS until the material at week 15
EXAMPLE OF QUIZ QUESTIONS 1. Complete the following system of linear equation with the Gaussian / Gauss Jordan elimination
𝑥 2𝑧 7𝑢 11
2𝑥 𝑦 3𝑧 4𝑢 9
3𝑥 3𝑦 𝑧 5𝑢 8
2𝑥 𝑦 4𝑧 4𝑢 10 2. Given the following system of linear equation
a. Determine the value of 𝑎 for the system of linear equation above to have one solution b. Determine the value of a for the system of linear equation above to have many solutions c. Determine the value of a for the system of linear equation above to have no one solution 3. Given 𝐴
1 0 1 0 1 1 1 1 0
a. Determine 𝐴
b. Complete the linear equation 𝐴𝑋 𝐵 if 𝐵 1 2 1
4. Determine
0 5 5 5
1 100 50
0
100 0 0
5. If 𝐴
𝑎 𝑏 𝑐 𝑑 𝑒 𝑓
𝑔 ℎ 𝑖 and det 𝐴 = 4
a. Determine det 4𝐴
b. Determine
𝑎 𝑑 𝑎 𝑑 𝑔
𝑏 𝑒 𝑏 𝑒 ℎ
𝑐 𝑓 𝑐 𝑓 𝑖
SAMPLE HOW TO ASSESS NO 2
STEPS STEPS SKOR
I
Student able to make augmented matrix
1 2 3
3 1 5
4 1 𝑎 14
4 2
𝑎 2
4
II Students are able to use Elementary Linear Operations to change the augmented matrix into a lower triangle matrix
1 2 3
3 1 5
4 1 𝑎 14
4 2
𝑎 2
𝑂𝐵𝐸 ∶ 𝐵 3𝐵 𝑎𝑛𝑑 𝐵 4𝐵 1 2 3
0 7 14
0 7 𝑎 2
4 10
𝑎 14
𝑂𝐵𝐸: 𝐵 𝑥
1 2 3
0 1 2
0 7 𝑎 2
104 𝑎 714
𝑂𝐵𝐸 ∶ 𝐵 7𝐵 1 2 3
0 1 2
0 0 𝑎 16
104 𝑎74
4
III a. Students are able to determine the conditions for the above system of linear equation to have one solution Condition : 𝑎 16 0
Answer : 𝑎 4, 4
4
IV b. Students are able to determine the conditions for the system of linear equation above to have many solutions
Condition : 𝑎 16 0 dan 𝑎 4 0 Answer : 𝑎 4
4
v c. Students are able to determine the conditions for the system of linear equation above to have no solutions Condition : 𝑎 16 0 dan 𝑎 4 0
Answer : 𝑎 4
4
Study Program Name Bachelor, Mathematics Department, FMKSD-ITS Course Name Elementary Linear Algebra
Course Code KM184203
Semester 2
Sks 4
Supporting Lecturer Dian Winda S, SSi, MSi
Materials • Matrices and Vectors
• Vector Space
• Transformation Learning
Outcome
[C2] Able to explain basic concepts of mathematics that includes the concept of a proof construction both logically and analytically, modeling and solving the simple problems, as well as the basic of computing.
[C3] Able to solve problems based on theoretical concepts in at least one field of mathematics:
analysis and algebra, modeling and system optimization, and computing science.
COURSE LEARNING OUTCOME
1. Students are able to follow developments and apply math and be able to communicate actively and correctly either oral or written
2. Students are able to explain intelligently and creatively about the significant role of ALE applications in the field of related knowledge clusters and other fields
3. Students have a special ability and able to process their ideas enough to support the next study in accordance with the related field
4. Students are able to present their knowledge in ALE independently or in teamwork
Meets Sub Course Learning Outcome
Breadth of Materials Learning Methods Time Estimatio
n
Student Learning Experiences
Assessment Criteria and Indicator
Weigh ing Assess
ment (%) 1-4 • Students are able to
complete the SPL by the Gaussian or Gauss Jordan elimination method And able to explain why SPL has no settlement.
• Students are able to use operations on the matrix and understand the algebraic properties of the matrix
• The understanding of SPL and Matrix is enlarged
• Elementary Line Operation (OBE)
• Gaussian and Gauss Jordan elimination
• Operation Matrix
• Properties of Algebra In Matrices
.
[Ref. 1 page: 9-98]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion,
4x(2x50’)
TaSks Exercise
questions • Accuracy defines SPL and
enlarged matrix.
• Ability to complete SPL with OBE
• Be able to complete SPL using Gaussian and Gauss Jordan
• Be able to explain the properties of algebra in the matrix
15%
5-6 • Students are able to find inverse matrix, can complete SPL with inverse matrix
• Students recognize the types of matrices and properties of the matrix
• Looking for Inverse matrix
• Complete the SPL with the inverse matrix
• Matrix type: Diagonal matrix, triangular matrix, symmetry matrix and its properties [Ref. 1 page: 99-139]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) TaSks Exercise
questions • Be able to get the inverse of a matrix
• Able to complete SPL with inverse matrix
• Be able to explain the types and properties of the matrix
5%
7-8 • Students are able to find the determinant of a matrix with Cofactor expansion
• Students are able to find the determinant of a matrix by Row Reduction
• Students are able to understand the properties of the determinant
• Students are able to complete the SPL with the cramer's rules
• Counting determinants with Cofactor expansion
• Counting determinants by Reducing Rows
• the properties of the determinant
• complete SPL with cramer rules [Ref. 1 page: 173-211]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) TaSks Exercise
questions • Able to calculate determinants with Cofactor expansion
• Capable of Counting determinants by Row Reduction
• Be able to explain the properties of the determinant
• Able to complete SPL with cramer rules
10%
9-12 Students are able to understand the vectors in space 2, space 3 and space n and operation on the vector
Students are able to define norm, product of point (product dot), distance, cross product, orthogonal set at R ^ n, seta geometry from linear System
vector in space 2, space 3 and space n
operation on the vector norm, dot product, distance, cross product, orthogonal set at R ^ n, set geometry of linear system [Ref. 1 page: 226-320]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) TaSks Exercise
questions Able to explain vectors in space 2, space 3 and space n
Be able to explain the operation on the vector
Ability to explain and norm, product of point (product dot), distance, cross product, orthogonal set at R ^ n, seta geometry of linear System
15%
13,14 • Students are able to understand real vector spaces
• Students are able to understand the real vector subspace
• Students are able to understand linear and linearly independent combinations
• real vector space
• real vector subspace
• linear and linearly independent combinations
[Ref. 1 page: 328-375]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) TaSks Exercise
questions • Be able to explain real vector spaces and real vector subspaces
• Be able to explain linear combinations and linearly independent sets
5%
15,16 Midterm Exam
17-19 • Students are able to understand the basis and dimension of a vector space
• Students are able to determine the relative coordinates of a vector on a basis in a vector space
• Students are able to understand the row space, column space, blank space, rank, nullity of a matrix
• Base
• The vector space dimension
• Relative Coordinates
• Transition Matrix
• Classroom, Column Room, Empty Room
• Rank and nullity [Ref. 1 page: 377-455]
• Lectures,
• Student conditioning,
• Question and answer.
• Giving exercise
• Group discussion
2x(2x50’) TaSks Exercise
questions • able to explain the basis and dimension of a vector space
• able to determine the relative coordinates of a vector to a basis in a vector space
• able to explain the row space, column space, empty space, rank, nullity of a matrix
15%