MATHEMATICS IN THE MODERN WORLD - FCAMPENA
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMMathematics in the Modern WorldMATHEMATICS IN THE MODERN WORLDCourse SyllabusLead Department:College:Course Code:Mathematics and Statistics DepartmentCollege of ScienceGEMATMWClass 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 aestheticdimensions. It includes the study of the nature of mathematics and how the perception of this leads to different tools for understandingand dealing with various aspects of present day living such as managing personal finances, making social choices, appreciating geometricdesigns, 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 thinkerEffective communicatorReflective lifelong learnerDemonstrate knowledge and skills in mathematics to analyze personal and social problems throughthe use of mathematical tools and to explain and present solutions effectively in written or oralform.MAY2018nocone/ocampos/cantubar1
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMMathematics in the Modern WorldII. FINAL COURSE OUTPUT:As evidence of attaining the above learning outcomes, the student is required to do and submit the following during theindicated dates of the term.LEARNING OUTCOMEREQUIRED OUTPUTDemonstrate knowledge and skills in mathematics toanalyze personal and social problems through the useof mathematical tools and to explain and presentsolutions effectively in written or oral form. Individual Output Group OutputDUE DATEWhenever possible, the students will involve inputs from industry practioners in order for them to see real-lifeapplications 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 models2. The group learning output should exhibit the use of mathematical reasoning, writing and proving in tacklingsolutions to a range of issues encompassing social, political, economic and financial aspects or involving naturalsciences, technology and the arts.3. Each learning output may be presented in any of the following forms. Infographics Digital Stories Dance ChoreographyMAY2018nocone/ocampos/cantubar2
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUM Mathematics in the Modern WorldArt DesignMini-magazine (collection of at least 3 articles)Song/Rap/PoemStoryboard/ComicsPlay (Script, Act)III. RUBRIC FOR ASSESSMENT:CRITERIAUnderstanding ofmathematicalconcepts(REASONING)25%Justification OPINGBEGINNINGShows completeand in-depthunderstanding ofthe underlyingmathematicalconcepts andprinciples neededto tackle conceptsand solve problemsShows nearlycompleteunderstanding of theproblem’smathematicalconcepts andprinciples.Shows someunderstanding of themathematicalconcepts andprinciples needed tosolve the problem.Shows very limitedor minimalunderstanding ofthe problem’smathematicalconcepts andprinciples.Demonstrateslogical and validreasoning inpresenting allarguments thatcover the conceptsdiscussedDemonstrates logicaland valid reasoningin presenting allarguments that coverthe conceptsdiscussed except for afew minor errorsDemonstrates logicaland valid reasoningin some argumentsthat cover theconcepts discussedbut there are somemajor errors in thediscussionsDemonstratesillogical and invalidreasoning in manyarguments.MAY2018nocone/ocampos/cantubar3
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMCRITERIAEXCEPTIONALClarity of Explanation Explanation iswell-written,(WRITING IN MATH)complete andunambiguous.25%Terminologies andsymbols are usedcorrectly.Integration with other Presents conceptsdisciplinesthat make use of atleast two pectives, andshows deep25%understanding ofmathematics as atool in thesedisciplines throughinnovativeconnections amongor solutions basedon /cantubarMathematics in the Modern WorldSATISFACTORYDEVELOPINGBEGINNINGExplanation is clearbut few simpledetails are missed.Terminologies andsymbols are usedappropriately.Explanation isambiguous and quitedifficult tounderstand. Somesymbols andnotations are usedinappropriately.Presents conceptsthat make use of atleast one otherdisciplinalperspective but somedetails areinaccurately statedExplanation isdifficult tounderstand,ambiguous andincomplete.Presents conceptsthat make use of atleast two otherdisciplinalperspectives andshows substantialunderstandingthrough innovativesolutions, but a fewdisciplinalconnections aremissed.Lacks presentationof concepts usingother disciplinalperspectives4
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMMathematics in the Modern WorldIV. 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 QuizzesAssignment and SeatworkBlog/JournalLearning Output1. Individual2. 5%25%100%5
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMMathematics in the Modern WorldVI. LEARNING PLAN:LEARNINGOUTCOMETOPICNo. s)Recognize reasoning andproof as fundamentalaspects of mathematics anduse one’s knowledge andskills in constructing aconvincing argument for thepurpose of solving aproblem0. Course Introduction1. Mathematics as aLanguageA. Logic and ReasoningB. Writing MathematicalProofsHow can I view mathematicsas a fundamental toolapplicable to a wide range ofdisciplines?13Student self-assessmentand reflectionSeatwork andAssignmentsSkills exercisesINDEPENDENTLEARNING:3 hours**Research on Logic Puzzlesand Math ProofsCullinane, ATransition toMathematics withProofsLogical Reasoning, pages69-98Nocon &Nocon,Essential Mathematicsfor the Modern World.Mathematical Language,MathematicalReasoning, pages 7-25Week 2 – 3Each student is to gather2-3 logic puzzles and 2mathematical proofs.After studying thesolutions of the selectedlogic puzzles and theproofs, the studentsubmits a paper thatMAY2018nocone/ocampos/cantubar6
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMLEARNINGOUTCOMEMathematics in the Modern WorldTOPICNo. s)explains the solutions andproof.Form a solid understandingof sound financial planningthat involves effectivemoney management andreasonable investmentschemes2. Mathematics in FinanceA. Personal Finances(savings,stocks and bonds,credit card)B. TaxationHow can I use mathematicsto gain financial literacy andprofitability?3Submission ofIndividual ProjectMoney-Savings BlogStudent self-assessmentand reflectionSeatwork andAssignmentsSkills exercisesFuscaldo, D. PersonalLoans 101: Everythingyou need to know.Nocon &Nocon,Essential Mathematicsfor the Modern World.Consumer Math, pages37-77INDEPENDENTLEARNING:4 hours**Virtual Stocks(Investagrams portfolio)Investment PlanWeek 1Each student is to createan Investagram account.With Php300,000 virtualmoney, s/he is to investMAY2018nocone/ocampos/cantubar7
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMLEARNINGOUTCOMEMathematics in the Modern WorldTOPICNo. s)in stocks and monitor hisprofit for a period of 45days.Week 4-5For the investment plan,the student conducts aresearch on the differentinvestment options thats/he can pursue. He is tosubmit his owninvestment plan detailingthe amounts ofinvestment and expectedreturns.Demonstrate understandingof the presence ofmathematics in nature andin the arts, and recognize theusefulness of patternrecognition in solving reallife problemsMAY2018nocone/ocampos/cantubar3. Mathematics in NaturalSciences and the ArtsA. Patterns and IsometriesB. Fibonacci Sequence andtheGolden RatioC. Fractals2Submission of InitialProject ProposalStudent self-assessmentand reflectionSkills exercisesTannenbaum,Excursions in ModernMathematicsSymmetry, pages 324339Fractals, pages 356-368Fibonacci, Golden Ratiopages 388-400INDEPENDENTLEARNING:Shesso, Math forMystics,Seatwork andAssignments8
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMLEARNINGOUTCOMEMathematics in the Modern WorldTOPICNo. s)How is mathematicsinvolved in the design ofcreative works?1 hour**Creative designs ofwallpaper, rosette or friezepatternsFibonacci, Golden Ratio,pages 101-108Week 6The student may createthe designs by hand orby using any application(e.g. Geogebra).Develop a repertoire of toolsand principles for analyzingconflicts and groupdecisions through the use ofmathematics4. Mathematics inDecisionSciencesA. GamesB. Social choicesHow can I usemathematics to aid inwise mission of FinalProject ProposalLong Quiz 1Film showingStudent self-assessmentand reflectionSeatwork andAssignmentsAngel & Porter, ASurvey ofMathematics withApplicationsVoting, pages 779-807Skills exercisesSobecki and Bluman,Mathematics in OurWorldVoting, pages 690-714INDEPENDENTLEARNING:2 hours**Position paperKolokoltsov andMalafeyev,Understanding GameTheory9
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMLEARNINGOUTCOMEMathematics in the Modern WorldTOPICNo. s)Week 7-8The students choose asituation that involvesconflict and analyze itusing the concept of gametheory. A written reportis a required output forthis group activity.Exhibit understanding of therole of mathematics indigital communicationsystems by constructingdiagrams that illustrate theprocesses of encodingdecoding and encryptiondecryption5. Mathematics inCommunicationTechnologiesA. Error Correction andDetectionB. Encryption andDecryptionHow is mathematics utilizedin the development of thedigital communicationsystem?3-4Project ProgressReport 1Student self-assessmentand reflectionSeatwork andAssignmentsSkills exercisesLaboratory workFilm showingINDEPENDENTLEARNING:2 hours**MAY2018nocone/ocampos/cantubarPrisoner’s Dilemma,pages 3-11Nocon &Nocon,Essential Mathematicsfor the Modern World.Games, pages 139-150Social Choices, 157-172Burger and Starbird,The Heart ofMathematics Bar Codes, pages 82-94Cryptography, pages 95106Nocon and Nocon,Essential Mathematicsfor the Modern WorldCommunicatingEfficiently, pages 89-105CommunicatingSecurely, pages 106-130Trappe andWashington,Introduction to10
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMLEARNINGOUTCOMEMathematics in the Modern WorldTOPICNo. s)Simulation on relatedalgorithmsWeek 10The student performsactual computations thatapply the RSACryptosystem inenciphering anddeciphering messages.Show understanding of howto improve the efficiency ofalgorithms by giving ananalysis and presenting asolution to a real lifeproblem6. Mathematics forEfficiencyA. Linear ProgrammingB. Shortest Path ProblemsC. Transportation andAssignment ProblemsHow can I usemathematics to efficientlymanage t ProgressReport 2Long Quiz 2Student self-assessmentand reflectionSeatwork andAssignmentsSkills exercisesLaboratory workINDEPENDENTLEARNING:2 hours**Cryptography withCoding TheoryCryptography, pages 1233, 137-140Coding Theory, pages295-301Nocon and Nocon,Essential Mathematicsfor the Modern WorldEfficiency, pages 189226Smith, The Nature ofMathematicsNetworks, GraphTheory, pages 407-431Linear Programming,pages 843-85011
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMLEARNINGOUTCOMEMathematics in the Modern WorldTOPICNo. s)Case study on applicationsto logistics and optimizationWeek 11-12For this group activity,students are asked toidentify one real lifeproblem and present itssolution using linearprogramming. It may alsobe an actualtransportation orassignment problem.Project ProgressReport 3Presentation of the FinalLearning OutputThe total number of meetings for discussions I have indicated above is 19 (max of 21). There are 2 meetings for the long testsand 1 meeting for the presentation/submission of final project. Hence, we have about 2-4 meetings allowance for classsuspensions and LASARE classes. This is really tight BUT there are some lessons that can be assigned to the students for selfstudy.VII. REFERENCESBooksMAY2018nocone/ocampos/cantubar12
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMMathematics in the Modern WorldAngel, 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 PublishingPlatform.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 ResourcesMAY2018nocone/ocampos/cantubar13
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMMathematics in the Modern WorldBrown, B. Prim's Algorithm: Minimal Spanning Tree. https://www.youtube.com/watch?v YyLaRffCdk4Fuscaldo, D. Personal Loans 101: Everything you need to know. Retrieved March 30, 2018 l-loans-101.aspx.Kenny, T. Differences between stocks and bonds. Retrieved March 30, 2018 from tocks-and-bonds-417069.Bitcoin: How Cryptocurrencies Work, https://www.youtube.com/watch?v kubGCSj5y3kCryptography: The Science of Making and Breaking Codes. https://www.youtube.com/watch?v -yFZGF8FHSg&t 58sDavid 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 46sGame Theory: The Science of Decision Making, https://www.youtube.com/watch?v MHS-htjGgSYLinear Programming: Introduction, http://www.purplemath.com/modules/linprog.htmThe Black Chamber, https://simonsingh.net/The Black Chamber/The enigma of WWII codebreaker Alan Turing https://www.youtube.com/watch?v nEomYB94TTIThe Enigma Machine Explained https://www.youtube.com/watch?v ASfAPOiq eQ158,962,555,217,826,360,000 (Enigma Machine) – Numberphile https://www.youtube.com/watch?v G2 Q9FoD-oQWhat is a Digital Signature? https://www.youtube.com/watch?v VIcBpRpiBocBlockchain tutorial 6: Digital signature https://www.youtube.com/watch?v OKg4PqD01Z0MAY2018nocone/ocampos/cantubar14
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMMathematics in the Modern WorldPublic Key Cryptography: RSA Encryption Algorithm https://www.youtube.com/watch?v wXB-V Keiu8&t 117sMathematics - The Language of the Universe - Full Documentary Films https://www.youtube.com/watch?v KWkQU99AoxgStock Markets in Plain English Animated https://www.youtube.com/watch?v ejjNMnIo3FgHow Your Money Grow With Stocks? https://www.youtube.com/watch?v oOKyFJFYKAStock Exchange Explained In 2 Minutes https://www.youtube.com/watch?v l3t406oTmssVIII. CLASSROOM POLICIES1. As a general policy, no special or make-up tests for missed exams will be given. However, a faculty member maygive special exams fora. approved absences (where the student concerned officially represented the University at some function oractivity).b. absences due to serious illness which require hospitalization, death in the family and other reasons whichthe 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 theexam) 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/cantubar15
DE LA SALLE UNIVERSITY MANILANEW LASALLIAN CORE CURRICULUMMathematics in the Modern World7. Students who wish to go to the washroom must politely ask permission and, if given such, they should be back inclass 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 ofgrades may be given as bonus points, based on recitation, assignments, board work and others.11. The percentage score conversion table isFinal Grade (%)EquivalentGrade PointDescription95 - 1004.089 - 943.5ExcellentSuperior83 - 883.0Very Good78 - 822.5Good72 - 772.0Satisfactory66 - 711.5Fair60 - 651.0Below 600.0PassedFailedMAY2018nocone/ocampos/cantubar16
Research on Logic Puzzles and Math Proofs 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 Cullinane, A Transition to Mathematics with Proofs Logical Reasoning, pages 69-98 Nocon &Nocon,
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Le genou de Lucy. Odile Jacob. 1999. Coppens Y. Pré-textes. L’homme préhistorique en morceaux. Eds Odile Jacob. 2011. Costentin J., Delaveau P. Café, thé, chocolat, les bons effets sur le cerveau et pour le corps. Editions Odile Jacob. 2010. Crawford M., Marsh D. The driving force : food in human evolution and the future.
