COURSE SYLLABUS

Course Title Combinatorial GeometryCourse Code GRMS No. of Units 3PrerequisiteProfessor E-mail AddressConsultation Time Day Place

I. COURSE DESCRIPTION

This is a course on Combinatorial Geometry. Basic principles in Combinatorics is taught here. Fundamental Principles of Counting such: Rules of Sum and Product, Permutation, Combinations, Binomial Theorem, Principle of Inclusion and Exclusion, Generating Functions and Recurrence Relations. Finally, these principles are applied in the field of Geometry (Euclidean or Non-Euclidean)

II. DESIRED LEARNING RESULTS

Expected Lasallian Graduate Attributes (ELGA) By the end of the course, the student will be able to:

God-LovingExhibit the spirit of Faith in God and on oneself by believing that even the most difficult problems can be learned and solved with hard work and honesty. Demonstrate the spirit of Zeal by responding positively and logically to mathematical problem solving by considering it as a blueprint of solving actual difficulties in the real world.

Manifest the spirit of Communion by synergistically cooperating with others, practicing initiative and helpfulness in accomplishing individual and group tasks.

Passion for Excellence Appreciate that attention to details and promptness are of prime importance in any mathematics course and mediocrity cannot be an acceptable trait.

Assure accuracy of concrete solution to real-life problems.

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PatrioticAnalyze and offer reasonable solution to prevalent community and national issues using an appropriate mathematical approach.

Recognize the need for balance between freedom of learning techniques and discovering solutions and responsibility of applying these in actual problems of the community and the nation as a whole.

III. FINAL PRODUCTAt the end of the course, students should be able to:

1. Define the fundamental principles of counting and apply them to some situations2. Differentiate between permutation and combination in the actual problems3. Introduce the principles of inclusion and exclusion4. Presents the same principle applied to various conditions5. Introduce the pigeon-hole principles6. Introduce varied examples in varied situations.7. prove some combinatorial properties which fundamentals and basics.8. Familiarize generating functions and its applications.9. Compare and contrast different kinds of recurrence relations.

VALID ASSESSMENT OF THE FINAL PRODUCT

ELGA: GOD LOVING

CRITERIA LEVEL III (3) LEVEL II (2) LEVEL I (1) SCOREAttitude towards finding the solution to the defined problem

Highly positive and confident trusting that God guided them solve the problem

With some level of optimism and confidence

Very negative view and indifferent

Involvement of self and others in gathering factual and valid data

Evidently resulted from a concerted effort

With acceptable degree of assistance in data gathering/processing

Very minimum contribution to data gathering/processing

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ELGA: PASSION FOR EXCELLENCECRITERIA LEVEL III (3) LEVEL II (2) LEVEL I (1) SCORE

Organization and coherence of presentation and promptness in submission

Discussion is very logical and coherent. Problem sets were submitted on time.

Discussion is very logical and coherent but problem sets were not submitted on time.

Discussion is not very logical and incoherent. Problem sets were not submitted on time.

Accuracy and correctness of outputs.

Mathematical proofs and constructions are accurate and general.

Mathematical proofs and constructions are not very accurate or not general.

Mathematical proofs and constructions are not accurate and not general.

ELGA: PATRIOTIC

CRITERIA LEVEL III (3) LEVEL II (2) LEVEL I (1) SCOREThe use of mathematical knowledge in nation-building.

A high appreciation of the usefulness of mathematics learned in this subject, with respect to solving real-life problems in our community.

A moderate appreciation of the usefulness of mathematics learned in this subject, with respect to solving real-life problems in our community.

A low appreciation of the usefulness of mathematics learned in this subject, with respect to solving real-life problems in our community.

Utility of the subject in teaching college students.

High level of applicability of knowledge in improving the teaching of college mathematics.

Moderate level of applicability of knowledge in improving the teaching of college mathematics.

Low level of applicability of knowledge in improving the teaching of college mathematics.

IV. ASSESSMENT

GRADING SYSTEM

CRITERIA PERCENTAGEMidterm ExamProblem Sets/Attendance (Problem sets are equivalent to a LQ)Home Works/ Seat Works/Reports and ParticipationsFinal ExamsTOTAL

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V. COURSE OUTLINE

TOPICS HOURS TEACHING STRATEGY LEARNING ACTIVITIES1. Fundamental Principles of

Counting1.1 Rules of sum and product1.2 Permutations1.3 Combinations: the binomial

Theorems1.4 Combinations with repetitions

9 Lectures, seatwork, discussion, assignments, drills and practice exercises (either alone, in pairs or in groups)

Class interactionBoard exercisesIndependent research work

Long Quiz 1 3

2. Principle of Inclusion and Exclusion2.1 Pigeon-Hole Principle2.2 Generalizations of the Pigeon-

Hole Principle

9 Lectures, seatwork, discussion, assignment, drills and practice exercises (either alone, in pairs or in groups)

Class interactionBoard exercises

Long Quiz 2 33. Generating Functions

3.1 Introductory Examples.3.2 Calculation techniques3.3 Partitions of Integers3.4 Exponential Generating

Functions3.5 Summation Operator

9 Lectures, seatwork, discussion, assignment, drills and practice exercises (either alone, in pairs or in groups)

Class interactionBoard exercises

Midterm Examination 3 Sit-in written exam

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TOPICS HOURS TEACHING STRATEGY LEARNING ACTIVITIES4. Recurrence Relations

4.1 First-Order Linear Recurrence Relation

4.2 Second-Order Linear Homogeneous Recurrence Relation with Constant Coefficients

4.3 Nonhomogeneous Recurrence Relation

4.4 Method of Generating Functions

9Prayer, lectures, seatwork, discussion, assignment, drills and practice exercises (either alone, in pairs or in groups)

Class interactionBoard exercisesResearch work

5. Applications to Geometry 5.1 Counting Points 5.2 Counting Lines 5.3 Counting Regions 5.5 Counting Configurations 5.6 Counting Paths

6 Reporting. Each student is given a part to report

Final Examination 3 Sit-in Exam

VI. COURSE POLICIESA. The maximum allowable number of hours of absences inclusive of tardiness is 9. All absences after that shall mean excessive

absences and a grade of NC. Refer to policies on attendance in your student handbook.B. Problem sets should be submitted after the attendance is checked or as specified by your teacher. C. An approved absence shall be treated accordingly based on the provisions on your student handbook. You have to inform your

teacher immediately upon return to school to set a schedule for this purpose. D. Special major exams are scheduled one week after the administration of the major exams. Refer to the policies on special major

exams in your student handbook.E. Cheating will not be tolerated. Refer to policies on cheating in your student handbook.F. Instructors/Professors are not authorized to collect any cash from the students for any purpose (i.e., material reproduction of notes or

test papers, cost of field trips). When necessary, all payments must be coursed through any of your class officers or through the Accounting Office.

G. Classroom Courtesy:1. The use of cellular phones and other electronic gadgets during class hours and examination are prohibited unless a

special permission is sought.2. Wearing of caps inside the classroom is prohibited.

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VII. REFERENCES

Textbook: Grimaldi, Ralph P., Discrete and Combinatorial Mathematics-An Applied Introduction, Fifth Edition, Pearson-Addison Wesley, USA

References: 1. Graham, R. L.,et al (1995). Handbook in Combinatorics. Elsevier Amsterdam, UK.2. Hugo Hadwiger and Hans Hebrunner. (2003). Combinatorial Geometry in the Plane, Holt, Rinehart and Winston, New York, USA3. Szilard, AndrasA. (2007) Elementary Combinatorial Geometry Problem and Solution, Gil Publishing House, Romania. 4. V.K. Balakrisnan. (1995). Combinatorics Schaum’s Outlines, Schaum’s Outlines Series McGraw-Hill INC. San Francisco, USA

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