| １． |
Outline |
|
In this course, students learn the basics of mathematics which are necessary to learn subjects in science and engineering in Universities, especially, the basics of mathematics which are necessary to understand
subjects in computer science or electronics/electrical engineering.
The set theory is the base of mathematics learned in Universities. Based on the set theory, students will
learn mathematics, such as, the algebraic system, the mathematical analysis or geography in Universities.
Logic is necessary for computer programmings or the design of logical circuits.
The concept of induction or reduction, basic proof techniques and basic algebraic is required to understand the basics of computer science.
This course aims at learning the mathematical topics described above.
Students acquire skills related to the diplomatic policy, DP3, DP4C and DP4D.
<Comments>
訂正無し
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| ２． |
Objectives |
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The goal of this class is that students master the following abilities;
Students can explain the definition of basic logical operations, logical functions.
Students can construct a truth table given a logical function.
Students can find a canonical form of a logical function.
Students can construct a Karnaugh map from a truth table, then, simplify the logical function corresponding to the truth table, by using the Karnaugh map.
Students can show some logical functions which are corresponding to a implication.
Students can show the converse, the converse of contraposition and the contraposition given an implication,
and explain the equivalence of the implication and the controposition.
Students can explain the necessity condition, the sufficient condition and the necessity and sufficient condition given a proposition which includes implication.
Students can use the De Morgan's law both in the proposional logic and the predict logic.
Students can express a set by choosing the extensional or intentional notation appropriately.
Students can compute union, intersection, complement, difference and the power given sets.
Students can express the relation of sets by the Venn diagram or the relation of sets in the Venn diagram by using set operations.
Students can express the basics features of maps or functions.
Students can compute the union and the intersection of relations.
Students can express the definition of the equivalence relation and explain the feature of the equivalence relation.
Students can express the recursive definition, the mathematical induction, and the recursive algorithm.
Students can explain the features of basics algebraic structures, such as semi-groups, monoids, groups, rings and fields.
Students can find an identity element, an inverse element or a complement if they exist, given a operation table of an algebraic structure.
Students can explain the basic features of ordered relations, ordered sets or the Boolean lattice.
<Comments>
The goal of this class is that students master the following abilities;
Students can explain the definition of basic logical operations, logical functions.
Students can construct a truth table given a logical function.
Students can find a canonical form of a logical function.
Students can construct a Karnaugh map from a truth table, then, simplify the logical function corresponding to the truth table, by using the Karnaugh map.
Students can show some logical functions which are corresponding to a implication.
Students can show the converse, the converse of contraposition and the contraposition given an implication,
and explain the equivalence of the implication and the controposition.
Students can explain the necessity condition, the sufficient condition and the necessary and sufficient condition given a proposition which includes implication.
Students can use the De Morgan's law both in the propositional logic and the predicate logic.
Students can express a set by choosing the extensional or intentional notation appropriately.
Students can compute union, intersection, complement, difference and the power given sets.
Students can express the relation of sets by the Venn diagram or the relation of sets in the Venn diagram by using set operations.
Students can express the basics features of maps or functions.
Students can compute the union and the intersection of relations.
Students can express the definition of the equivalence relation and explain the feature of the equivalence relation.
Students can express the recursive definition, the mathematical induction, and the recursive algorithm.
Students can explain the features of basics algebraic structures, such as semi-groups, monoids, groups, rings and fields.
Students can find an identity element, an inverse element or a complement if they exist, given a operation table of an algebraic structure.
Students can explain the basic features of ordered relations, ordered sets or the Boolean lattice.
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| ３． |
Grading Policy |
|
Grading policy:
Midterm report(50%), Examination(50%).
The way of feedback;
Answers for questions or feedback for the contents of class, worksheets, and examination will be given in a class, through LMS or in office hours.
<Comments>
訂正無し
|
| ４． |
Textbook and Reference |
|
Text: 小倉久和著、"離散数学への入門、わかりやすい離散数学、" 近代科学社、2005.
ISBN-13: 978-4764903210
Teaching materials: Published through LMS.
<Comments>
訂正無し
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| ５． |
Requirements (Assignments) |
|
Before a class, students are required to prepare the class by using materials, such as slides, handouts and
related materials which will be published on the LMS, which requires about 1.5 hours.
In a class, students should concentrate on, not to take notes, but to understand the contents of class,
to solve exercises in a class,
because most of the materials were published on the LMS before the class and students can bring them with
tablets or smart phones.
After a class, students are required to review the materials used in the class or quizzes on the LMS, which requires about 1.5 hours.
<Comments>
Before the class, students are required to prepare by using materials, such as slides, handouts and
related materials which will be published on the LMS, which requires about 1.5 hours.
In the class, students should not concentrate on taking notes, but on understanding the contents. And concentrate on solving exercises in the class.
Because most of the materials are published on the LMS before the class and students can bring them with
tablets or smart phones.
After the class, students are required to review the materials used in the class or quizzes on the LMS, which requires about 1.5 hours.
|
| ６． |
Note |
|
Students can hardly earn credits not submitting the mid-term report. Thus, it is expected students to observe the deadline.
As for the self-learning support students are expected to utilize materials, such as slides, handouts and quizzes on the LMS
Before this course, it is required for students to learn mathematics in high school.
At the same semester with this course, students should take the following courses;
Programming 1, Linear Algebr.
<Comments>
Before a class, students are required to prepare the class by using materials, such as slides, handouts and related materials which will be published on the LMS, which requires about 1.5 hours.
In a class, students should concentrate on, not to take notes, but to understand the contents of class, to solve exercises in a class, because most of the materials are published on the LMS before the class and students can bring them with tablets or smartphones.
After a class, students are required to review the materials used in the class or quizzes on the LMS, which requires about 1.5 hours.
After this course, students should take Discrete Mathematics, Information Theory and courses which relate to computer and programming.
If a student has a question on quizzes or mid-term report or examinations, ask the question in the class or in office hours or through LMS.
This course is a required course, and relates to the mid term 3-1 of the attaining targets for learning and educating, in the JABEE program.
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| ７． |
Schedule |
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１. Logics and proofs 1 -propositions, predicates-
<Comments>
訂正無し |
２. Logics and proofs 2 -logical operators, truth table-
<Comments>
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３. Logics and proofs 3 -completeness of logical operation, functional completeness sets-
<Comments>
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４. Logics and proofs 4 -implication, contraposition, converse, converse of contraposition, necessary condition, sufficient condition if-and-only-if (iff), proof by contradiction-
<Comments>
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５. Canonical forms of logical functions, Disjunctive normal form, Conjunctive normal form
<Comments>
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６. Simplification of logical functions, Karnaugh map
<Comments>
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７. Two's complement of a number, Set theory 1
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８. Set theory 2
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９. Map, function, injective, surjective bijective,
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10. Induction, recursion, mathematical induction, recursive definition, recursive algorithm
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11. Relation 1, union of relations, intersection of relations
<Comments>
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12. Relation 2, a matrix of a relation, transitive relation, equivalence relation
<Comments>
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13. Algebraic systems, group, ring, field
<Comments>
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14. Ordered sets, lattice, Boolean lattice
<Comments>
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15. Summary and examination
<Comments>
訂正無し |
|
| １． |
Outline |
|
In this course, students learn the basics of mathematics which are necessary to learn subjects in science and engineering in Universities, especially, the basics of mathematics which are necessary to understand
subjects in computer science or electronics/electrical engineering.
The set theory is the base of mathematics learned in Universities. Based on the set theory, students will
learn mathematics, such as, the algebraic system, the mathematical analysis or geography in Universities.
Logic is necessary for computer programmings or the design of logical circuits.
The concept of induction or reduction, basic proof techniques and basic algebraic is required to understand the basics of computer science.
This course aims at learning the mathematical topics described above.
Students acquire skills related to the diplomatic policy, DP3, DP4C and DP4D.
<Comments>
訂正無し
|
| ２． |
Objectives |
|
The goal of this class is that students master the following abilities;
Students can explain the definition of basic logical operations, logical functions.
Students can construct a truth table given a logical function.
Students can find a canonical form of a logical function.
Students can construct a Karnaugh map from a truth table, then, simplify the logical function corresponding to the truth table, by using the Karnaugh map.
Students can show some logical functions which are corresponding to a implication.
Students can show the converse, the converse of contraposition and the contraposition given an implication,
and explain the equivalence of the implication and the controposition.
Students can explain the necessity condition, the sufficient condition and the necessity and sufficient condition given a proposition which includes implication.
Students can use the De Morgan's law both in the proposional logic and the predict logic.
Students can express a set by choosing the extensional or intentional notation appropriately.
Students can compute union, intersection, complement, difference and the power given sets.
Students can express the relation of sets by the Venn diagram or the relation of sets in the Venn diagram by using set operations.
Students can express the basics features of maps or functions.
Students can compute the union and the intersection of relations.
Students can express the definition of the equivalence relation and explain the feature of the equivalence relation.
Students can express the recursive definition, the mathematical induction, and the recursive algorithm.
Students can explain the features of basics algebraic structures, such as semi-groups, monoids, groups, rings and fields.
Students can find an identity element, an inverse element or a complement if they exist, given a operation table of an algebraic structure.
Students can explain the basic features of ordered relations, ordered sets or the Boolean lattice.
<Comments>
The goal of this class is that students master the following abilities;
Students can explain the definition of basic logical operations, logical functions.
Students can construct a truth table given a logical function.
Students can find a canonical form of a logical function.
Students can construct a Karnaugh map from a truth table, then, simplify the logical function corresponding to the truth table, by using the Karnaugh map.
Students can show some logical functions which are corresponding to a implication.
Students can show the converse, the converse of contraposition and the contraposition given an implication,
and explain the equivalence of the implication and the controposition.
Students can explain the necessity condition, the sufficient condition and the necessary and sufficient condition given a proposition which includes implication.
Students can use the De Morgan's law both in the propositional logic and the predicate logic.
Students can express a set by choosing the extensional or intentional notation appropriately.
Students can compute union, intersection, complement, difference and the power given sets.
Students can express the relation of sets by the Venn diagram or the relation of sets in the Venn diagram by using set operations.
Students can express the basics features of maps or functions.
Students can compute the union and the intersection of relations.
Students can express the definition of the equivalence relation and explain the feature of the equivalence relation.
Students can express the recursive definition, the mathematical induction, and the recursive algorithm.
Students can explain the features of basics algebraic structures, such as semi-groups, monoids, groups, rings and fields.
Students can find an identity element, an inverse element or a complement if they exist, given a operation table of an algebraic structure.
Students can explain the basic features of ordered relations, ordered sets or the Boolean lattice.
|
| ３． |
Grading Policy |
|
Grading policy:
Midterm report(50%), Examination(50%).
The way of feedback;
Answers for questions or feedback for the contents of class, worksheets, and examination will be given in a class, through LMS or in office hours.
<Comments>
訂正無し
|
| ４． |
Textbook and Reference |
|
Text: 小倉久和著、"離散数学への入門、わかりやすい離散数学、" 近代科学社、2005.
ISBN-13: 978-4764903210
Teaching materials: Published through LMS.
<Comments>
訂正無し
|
| ５． |
Requirements (Assignments) |
|
Before a class, students are required to prepare the class by using materials, such as slides, handouts and
related materials which will be published on the LMS, which requires about 1.5 hours.
In a class, students should concentrate on, not to take notes, but to understand the contents of class,
to solve exercises in a class,
because most of the materials were published on the LMS before the class and students can bring them with
tablets or smart phones.
After a class, students are required to review the materials used in the class or quizzes on the LMS, which requires about 1.5 hours.
<Comments>
Before the class, students are required to prepare by using materials, such as slides, handouts and
related materials which will be published on the LMS, which requires about 1.5 hours.
In the class, students should not concentrate on taking notes, but on understanding the contents. And concentrate on solving exercises in the class.
Because most of the materials are published on the LMS before the class and students can bring them with
tablets or smart phones.
After the class, students are required to review the materials used in the class or quizzes on the LMS, which requires about 1.5 hours.
|
| ６． |
Note |
|
Students can hardly earn credits not submitting the mid-term report. Thus, it is expected students to observe the deadline.
As for the self-learning support students are expected to utilize materials, such as slides, handouts and quizzes on the LMS
Before this course, it is required for students to learn mathematics in high school.
At the same semester with this course, students should take the following courses;
Programming 1, Linear Algebr.
<Comments>
Before a class, students are required to prepare the class by using materials, such as slides, handouts and related materials which will be published on the LMS, which requires about 1.5 hours.
In a class, students should concentrate on, not to take notes, but to understand the contents of class, to solve exercises in a class, because most of the materials are published on the LMS before the class and students can bring them with tablets or smartphones.
After a class, students are required to review the materials used in the class or quizzes on the LMS, which requires about 1.5 hours.
After this course, students should take Discrete Mathematics, Information Theory and courses which relate to computer and programming.
If a student has a question on quizzes or mid-term report or examinations, ask the question in the class or in office hours or through LMS.
This course is a required course, and relates to the mid term 3-1 of the attaining targets for learning and educating, in the JABEE program.
|
| ７． |
Schedule |
|
１. Logics and proofs 1 -propositions, predicates-
<Comments>
訂正無し |
２. Logics and proofs 2 -logical operators, truth table-
<Comments>
訂正無し |
３. Logics and proofs 3 -completeness of logical operation, functional completeness sets-
<Comments>
訂正無し |
４. Logics and proofs 4 -implication, contraposition, converse, converse of contraposition, necessary condition, sufficient condition if-and-only-if (iff), proof by contradiction-
<Comments>
訂正無し |
５. Canonical forms of logical functions, Disjunctive normal form, Conjunctive normal form
<Comments>
訂正無し |
６. Simplification of logical functions, Karnaugh map
<Comments>
訂正無し |
７. Two's complement of a number, Set theory 1
<Comments>
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８. Set theory 2
<Comments>
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９. Map, function, injective, surjective bijective,
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10. Induction, recursion, mathematical induction, recursive definition, recursive algorithm
<Comments>
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11. Relation 1, union of relations, intersection of relations
<Comments>
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12. Relation 2, a matrix of a relation, transitive relation, equivalence relation
<Comments>
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13. Algebraic systems, group, ring, field
<Comments>
訂正無し |
14. Ordered sets, lattice, Boolean lattice
<Comments>
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15. Summary and examination
<Comments>
訂正無し |
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