1 MATHEMATICS IN THE MODERN WORLD Course Syllabus Lead Department: College: Course Code: Mathematics and Statistics Department College of Science GEMA...

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Mathematics in the Modern World

MATHEMATICS IN THE MODERN WORLD Course Syllabus Lead Department: College: Course Code:

Mathematics and Statistics Department College of Science GEMATMW

Class Days and Time: Team Instructors:

Room: Consultation Hours:

ESTIMATED TIME FOR STUDY OF A LEARNING UNIT OUTSIDE CLASS:

________

14 HRS** (See Independent Learning Time Allocation)

I. COURSE DESCRIPTION: This course aims to discuss the nature of mathematics leading to appreciation of its practical, intellectual, social, and aesthetic dimensions. It includes the study of the nature of mathematics and how the perception of this leads to different tools for understanding and dealing with various aspects of present day living such as managing personal finances, making social choices, appreciating geometric designs, understanding codes used in data transmissions and security, and dividing limited resources fairly. UNIVERSITY ELGA:

LEARNING OUTCOMES (LO): On completion of the course, the student is expected to be able to:

Critical thinker Effective communicator Reflective lifelong learner

Demonstrate knowledge and skills in mathematics to analyze personal and social problems through the use of mathematical tools and to explain and present solutions effectively in written or oral form.

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Mathematics in the Modern World

II. FINAL COURSE OUTPUT: As evidence of attaining the above learning outcomes, the student is required to do and submit the following during the indicated dates of the term. LEARNING OUTCOME

REQUIRED OUTPUT

Demonstrate knowledge and skills in mathematics to analyze personal and social problems through the use of mathematical tools and to explain and present solutions effectively in written or oral form.

•

Individual Output

•

Group Output

DUE DATE

Whenever possible, the students will involve inputs from industry practioners in order for them to see real-life applications of the mathematics they have learned in the course. 1. For the individual output, a student may choose from any of the following options. • Financial plan • Critique of a mathematician’s essay or book • Mathematical patterns in art designs • Analysis of the mathematics behind an engineering prototype, algorithm, or mathematical models 2. The group learning output should exhibit the use of mathematical reasoning, writing and proving in tackling solutions to a range of issues encompassing social, political, economic and financial aspects or involving natural sciences, technology and the arts. 3. Each learning output may be presented in any of the following forms. • Infographics • Digital Stories • Dance Choreography

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• • • • •

Mathematics in the Modern World

Art Design Mini-magazine (collection of at least 3 articles) Song/Rap/Poem Storyboard/Comics Play (Script, Act)

III. RUBRIC FOR ASSESSMENT: CRITERIA Understanding of mathematical concepts (REASONING) 25%

Justification of Approach (PROVING) 25%

EXCEPTIONAL

SATISFACTORY

DEVELOPING

BEGINNING

Shows complete and in-depth understanding of the underlying mathematical concepts and principles needed to tackle concepts and solve problems

Shows nearly complete understanding of the problem’s mathematical concepts and principles.

Shows some understanding of the mathematical concepts and principles needed to solve the problem.

Shows very limited or minimal understanding of the problem’s mathematical concepts and principles.

Demonstrates logical and valid reasoning in presenting all arguments that cover the concepts discussed

Demonstrates logical and valid reasoning in presenting all arguments that cover the concepts discussed except for a few minor errors

Demonstrates logical and valid reasoning in some arguments that cover the concepts discussed but there are some major errors in the discussions

Demonstrates illogical and invalid reasoning in many arguments.

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CRITERIA

EXCEPTIONAL Clarity of Explanation Explanation is well-written, (WRITING IN MATH) complete and unambiguous. 25% Terminologies and symbols are used correctly. Integration with other Presents concepts disciplines that make use of at least two other (INTERDISCIPLINARY disciplinal INTEGRATION) perspectives, and shows deep 25% understanding of mathematics as a tool in these disciplines through innovative connections among or solutions based on varied disciplinal perspectives

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Mathematics in the Modern World

SATISFACTORY

DEVELOPING

BEGINNING

Explanation is clear but few simple details are missed. Terminologies and symbols are used appropriately.

Explanation is ambiguous and quite difficult to understand. Some symbols and notations are used inappropriately. Presents concepts that make use of at least one other disciplinal perspective but some details are inaccurately stated

Explanation is difficult to understand, ambiguous and incomplete.

Presents concepts that make use of at least two other disciplinal perspectives and shows substantial understanding through innovative solutions, but a few disciplinal connections are missed.

Lacks presentation of concepts using other disciplinal perspectives

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IV. OTHER REQUIREMENTS AND ASSESSMENTS: Aside from the final output, the student will be assessed at other times during the term by the following: • Position Paper • Group Report (Case Study) • Long Quizzes • Assignment and Seatwork • Blog/Video Blog/Journal • Investagrams Virtual Stocks Portfolio (www.investagrams.com) V. GRADING SYSTEM: • • • •

Average of Quizzes Assignment and Seatwork Blog/Journal Learning Output 1. Individual 2. Group Total

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20% 15% 15% 25% 25% 100%

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VI. LEARNING PLAN: LEARNING OUTCOME

TOPIC

No. of Meetings

LEARNING ACTIVITIES

READINGS

(for Discussions)

Recognize reasoning and proof as fundamental aspects of mathematics and use one’s knowledge and skills in constructing a convincing argument for the purpose of solving a problem

0. Course Introduction 1. Mathematics as a Language A. Logic and Reasoning B. Writing Mathematical Proofs How can I view mathematics as a fundamental tool applicable to a wide range of disciplines?

1 3

Student self-assessment and reflection Seatwork and Assignments Skills exercises INDEPENDENT LEARNING: 3 hours** Research on Logic Puzzles and Math Proofs

Cullinane, A Transition to Mathematics with Proofs Logical Reasoning, pages 69-98 Nocon &Nocon, Essential Mathematics for the Modern World. Mathematical Language, Mathematical Reasoning, pages 7-25

Week 2 – 3 Each student is to gather 2-3 logic puzzles and 2 mathematical proofs. After studying the solutions of the selected logic puzzles and the proofs, the student submits a paper that

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Mathematics in the Modern World TOPIC

No. of Meetings

LEARNING ACTIVITIES

READINGS

(for Discussions) explains the solutions and proof.

Form a solid understanding of sound financial planning that involves effective money management and reasonable investment schemes

2. Mathematics in Finance A. Personal Finances (savings, stocks and bonds, credit card) B. Taxation How can I use mathematics to gain financial literacy and profitability?

3

Submission of Individual Project Money-Savings Blog Student self-assessment and reflection Seatwork and Assignments Skills exercises

Fuscaldo, D. Personal Loans 101: Everything you need to know. Nocon &Nocon, Essential Mathematics for the Modern World. Consumer Math, pages 37-77

INDEPENDENT LEARNING: 4 hours** Virtual Stocks (Investagrams portfolio) Investment Plan Week 1 Each student is to create an Investagram account. With Php300,000 virtual money, s/he is to invest

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Mathematics in the Modern World TOPIC

No. of Meetings

LEARNING ACTIVITIES

READINGS

(for Discussions) in stocks and monitor his profit for a period of 45 days. Week 4-5 For the investment plan, the student conducts a research on the different investment options that s/he can pursue. He is to submit his own investment plan detailing the amounts of investment and expected returns.

Demonstrate understanding of the presence of mathematics in nature and in the arts, and recognize the usefulness of pattern recognition in solving real life problems

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3. Mathematics in Natural Sciences and the Arts A. Patterns and Isometries B. Fibonacci Sequence and the Golden Ratio C. Fractals

2

Submission of Initial Project Proposal Student self-assessment and reflection

Skills exercises

Tannenbaum, Excursions in Modern Mathematics Symmetry, pages 324339 Fractals, pages 356-368 Fibonacci, Golden Ratio pages 388-400

INDEPENDENT LEARNING:

Shesso, Math for Mystics,

Seatwork and Assignments

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Mathematics in the Modern World TOPIC

No. of Meetings

LEARNING ACTIVITIES

READINGS

(for Discussions) How is mathematics involved in the design of creative works?

1 hour** Creative designs of wallpaper, rosette or frieze patterns

Fibonacci, Golden Ratio, pages 101-108

Week 6 The student may create the designs by hand or by using any application (e.g. Geogebra).

Develop a repertoire of tools and principles for analyzing conflicts and group decisions through the use of mathematics

4. Mathematics in Decision Sciences A. Games B. Social choices How can I use mathematics to aid in wise decision-making?

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Submission of Final Project Proposal Long Quiz 1 Film showing Student self-assessment and reflection Seatwork and Assignments

Angel & Porter, A Survey of Mathematics with Applications Voting, pages 779-807

Skills exercises

Sobecki and Bluman, Mathematics in Our World Voting, pages 690-714

INDEPENDENT LEARNING: 2 hours** Position paper

Kolokoltsov and Malafeyev, Understanding Game Theory

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Mathematics in the Modern World TOPIC

No. of Meetings

LEARNING ACTIVITIES

READINGS

(for Discussions) Week 7-8 The students choose a situation that involves conflict and analyze it using the concept of game theory. A written report is a required output for this group activity.

Exhibit understanding of the role of mathematics in digital communication systems by constructing diagrams that illustrate the processes of encodingdecoding and encryptiondecryption

5. Mathematics in Communication Technologies A. Error Correction and Detection B. Encryption and Decryption How is mathematics utilized in the development of the digital communication system?

3-4

Project Progress Report 1 Student self-assessment and reflection Seatwork and Assignments Skills exercises Laboratory work Film showing INDEPENDENT LEARNING: 2 hours**

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Prisoner’s Dilemma, pages 3-11 Nocon &Nocon, Essential Mathematics for the Modern World. Games, pages 139-150 Social Choices, 157-172

Burger and Starbird, The Heart of Mathematics … Bar Codes, pages 82-94 Cryptography, pages 95106 Nocon and Nocon, Essential Mathematics for the Modern World Communicating Efficiently, pages 89-105 Communicating Securely, pages 106-130 Trappe and Washington, Introduction to

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Mathematics in the Modern World TOPIC

No. of Meetings

LEARNING ACTIVITIES

READINGS

(for Discussions) Simulation on related algorithms Week 10 The student performs actual computations that apply the RSA Cryptosystem in enciphering and deciphering messages.

Show understanding of how to improve the efficiency of algorithms by giving an analysis and presenting a solution to a real life problem

6. Mathematics for Efficiency A. Linear Programming B. Shortest Path Problems C. Transportation and Assignment Problems How can I use mathematics to efficiently manage operations?

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Project Progress Report 2 Long Quiz 2 Student self-assessment and reflection Seatwork and Assignments Skills exercises Laboratory work INDEPENDENT LEARNING: 2 hours**

Cryptography with Coding Theory Cryptography, pages 1233, 137-140 Coding Theory, pages 295-301

Nocon and Nocon, Essential Mathematics for the Modern World Efficiency, pages 189226 Smith, The Nature of Mathematics Networks, Graph Theory, pages 407-431 Linear Programming, pages 843-850

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Mathematics in the Modern World TOPIC

No. of Meetings

LEARNING ACTIVITIES

READINGS

(for Discussions) Case study on applications to logistics and optimization Week 11-12 For this group activity, students are asked to identify one real life problem and present its solution using linear programming. It may also be an actual transportation or assignment problem. Project Progress Report 3 Presentation of the Final Learning Output

The total number of meetings for discussions I have indicated above is 19 (max of 21). There are 2 meetings for the long tests and 1 meeting for the presentation/submission of final project. Hence, we have about 2-4 meetings allowance for class suspensions and LASARE classes. This is really tight BUT there are some lessons that can be assigned to the students for selfstudy. VII. REFERENCES Books MAY2018nocone/ocampos/cantubar

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Mathematics in the Modern World

Angel, A., Abbott, C. and Runde, D. (2016). A Survey of Mathematics with Applications, Pearson. Burger, E. and Starbird, M. (2005). The Heart of Mathematics, An invitation to effective thinking. Key College Publishing. Cullinane, M. (2013). A Transition to Mathematics with Proofs. Jones & Bartnett Learning, LLC. Feder, J. (1998). Fractals. Plenum Press. Kappraff, J.(2001). Connections, The Geometric Bridge Between Art and Science. World Scientific Publishing Co. Pte. Ltd. Kolokoltsov, V. and Malafeyev, O. (2010). Understanding Game Theory. World Scientific. Lakatos, I. (2015). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press. Nocon, R. and Nocon, E. (2018). Essential Mathematics for the Modern World. C & E. Publishing House. Shesso, R. (2007). Math for Mystics, Red Wheel/Weiser, LLC. Sobecki, D. and Bluman A. (2015). Mathematics in Our World. McGraw-Hill. Smith, K. (2013). Mathematics, Its Power & Utility, Thomson Brooks/Cole. Sundstrom, T. (2007). Mathematical Reasoning, Writing and Proof. Pearson Education, Inc. Talwalkar, P. (2014). The Joy of Game Theory, an Introduction to Strategic Thinking, CreateSpace Independent Publishing Platform. Tannenbaum, P. (2018). Excursions in Modern Mathematics, Pearson Education, Inc. Trappe W. and Washington, L. (2002). Introduction to Cryptography with Coding Theory, Prentice-Hall, Inc.

Online Resources

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Brown, B. Prim's Algorithm: Minimal Spanning Tree. https://www.youtube.com/watch?v=YyLaRffCdk4 Fuscaldo, D. Personal Loans 101: Everything you need to know. Retrieved March 30, 2018 from https://www.bankrate.com/finance/loans/personal-loans-101.aspx. Kenny, T. Differences between stocks and bonds. Retrieved March 30, 2018 from https://www.thebalance.com/thedifference-between-stocks-and-bonds-417069. Bitcoin: How Cryptocurrencies Work, https://www.youtube.com/watch?v=kubGCSj5y3k Cryptography: The Science of Making and Breaking Codes. https://www.youtube.com/watch?v=-yFZGF8FHSg&t=58s David Bailey's World of Escher-like Tessellations, http://www.tess-elation.co.uk. Fibonacci Sequence: The Nature’s Code. https://www.youtube.com/watch?v=wTlw7fNcO-0&t=46s Game Theory: The Science of Decision Making, https://www.youtube.com/watch?v=MHS-htjGgSY Linear Programming: Introduction, http://www.purplemath.com/modules/linprog.htm The Black Chamber, https://simonsingh.net/The_Black_Chamber/ The enigma of WWII codebreaker Alan Turing https://www.youtube.com/watch?v=nEomYB94TTI The Enigma Machine Explained https://www.youtube.com/watch?v=ASfAPOiq_eQ 158,962,555,217,826,360,000 (Enigma Machine) – Numberphile https://www.youtube.com/watch?v=G2_Q9FoD-oQ What is a Digital Signature? https://www.youtube.com/watch?v=VIcBpRpiBoc Blockchain tutorial 6: Digital signature https://www.youtube.com/watch?v=OKg4PqD01Z0 MAY2018nocone/ocampos/cantubar

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Public Key Cryptography: RSA Encryption Algorithm https://www.youtube.com/watch?v=wXB-V_Keiu8&t=117s Mathematics - The Language of the Universe - Full Documentary Films https://www.youtube.com/watch?v=KWkQU99Aoxg Stock Markets in Plain English Animated https://www.youtube.com/watch?v=ejjNMnIo3Fg How Your Money Grow With Stocks? https://www.youtube.com/watch?v=_oOKyFJFYKA Stock Exchange Explained In 2 Minutes https://www.youtube.com/watch?v=l3t406oTmss

VIII. CLASSROOM POLICIES 1. As a general policy, no special or make-up tests for missed exams will be given. However, a faculty member may give special exams for a. approved absences (where the student concerned officially represented the University at some function or activity). b. absences due to serious illness which require hospitalization, death in the family and other reasons which the faculty member deems meritorious. 2. If the student has no valid reason for missing an exam (for example, the student was not prepared to take the exam) then the student receives 0% for the missed quiz. 3. Learning outputs are required and not optional to pass the course. 4. Mobile phones and other forms of communication devices should be on silent mode or turned off during class. 5. Students are expected to be attentive and exhibit the behavior of a mature and responsible individual during class. They are also expected to come to class on time and prepared. 6. Sleeping, bringing in food and drinks, and wearing a cap and sunglasses in class are not allowed. MAY2018nocone/ocampos/cantubar

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7. Students who wish to go to the washroom must politely ask permission and, if given such, they should be back in class within 5 minutes. Only one student at a time may be allowed to leave the classroom for this purpose. 8. Students who are absent from the class for more than 5 meetings will get a final grade of 0.0 in the course. 9. Only students who are officially enrolled in the course are allowed to attend the class meetings. 10. Upon the discretion of the faculty member, a maximum of 3% over and above the 100% criteria for computation of grades may be given as bonus points, based on recitation, assignments, board work and others. 11. The percentage score conversion table is

Final Grade (%)

Equivalent Grade Point

Description

95 - 100

4.0

89 - 94

3.5

Excellent Superior

83 - 88

3.0

Very Good

78 - 82

2.5

Good

72 - 77

2.0

Satisfactory

66 - 71

1.5

Fair

60 - 65

1.0

Below 60

0.0

Passed Failed

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