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Supporting :

Dalam dokumen Discussion - Practice - QUIZ (Halaman 34-65)

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

  √   

    √ 

            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

  √   

  √ 

            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

    √ 

  √ 

            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

      √    √ 

            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

  √    √ 

     

√ 

            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

Student able to make augmented matrix 

1 2 3

3 1 5

4 1 𝑎 14

4 2

𝑎 2

 

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

   

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 

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%

Dalam dokumen Discussion - Practice - QUIZ (Halaman 34-65)

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