Mathematics in the Modern World

Course Description

Mathematics in the Modern World is an interdisciplinary course intended for first year students of all courses.

This course aims to equip students with a fundamental appreciation of the role and function of mathematics as a field of study that systematically searches for truth and meaning in human life and existence.

It further seeks to enhance the students’ capacity in mathematical, algorithmic, and logical thinking in order to develop the students’ ability for argumentation, specifically textual argumentation, by identifying and analyzing logical fallacies.

This course also aims to develop among the students the value of critical yet prayerful reflection and discernment primarily in dealing with the application of mathematical principles in their personal lives and in contemporary social realities, especially in the context of Mindanao. Through this, the students will eventually contribute in the promotion of the common good, social justice, preferential option for the poor, peace-building and interreligious dialogue as future leaders of their respective communities.

Course Learning Outcomes (CO)

That the students will be able to deepen their appreciation for the useful and practical application of mathematics not just in their day-to-day undertakings but, more importantly, in analyzing and resolving the various contemporary concerns in the community using mathematical theories and methods.
That the students will be able to strengthen their commitment toward environmental stewardship as they reflect more deeply on the mathematical principles reflected in the mystery and beauty of nature and ecology.
That the students will be able to apply their learnings in Mathematics prudently as they deal with the challenges posed by the modern society.
Through the logical thinking and reflective activities in Mathematics in the Modern World, this course contributes to the holistic development of students through
- acquiring the skills necessary to demonstrate proficiency in selecting and utilizing mathematical tools and procedures;
- manifesting social justice and sensitivity in addressing contemporary and contextual issues and challenges;
- appreciating and nurturing the arts especially the arts of the indigenous people of Mindanao;
- handling of conflicts in peaceful ways for the common good locally, nationally and internationally;
- providing awareness and promoting care of the environment;
- recognizing natural phenomena, human inventions including structural designs and cultural productions and other ubiquitous occurrences especially in Mindanao; and
- equipping them with tools for making decisions pertaining to wealth creation and its equitable distribution as well as managing wisely personal finances.

Course References

Adam, J. A. (2013). Mathematics in nature: Modeling patterns in the natural world. New Jersey, USA: Princeton University Press.

Auffman, et al. (2018). Mathematics in the modern world. Manila, PH: Rex Book Store.

Ball, W. W. R. (1960). A short account of the history of mathematics. USA: Dover Publications, Inc.

Broverman, S. A. (2010). Mathematics of investment and credit, 5th ed. USA: ACTEX Publishing, Inc.

Cameron, P.J. (1999). Sets, logic and categories. London, UK: Springer.

Gonzalez, L. (2014). Golden ratio. In Salem Press Encyclopedia of Science. Research Starters.

Halmos, P.R. (1991). Naïve set theory. USA: Springer.

Hart, W.L. (1980). Mathematics of investment, 5th ed. D.C.: Heath and Company.

Malkevitch, J. et al. (1988). For all practical purposes: Introduction to contemporary mathematics, 2nd ed. New York: W. H. Freeman and Company.

Nocon, E. and Nocon, R. (2016). Essential mathematics for the modern world. Quezon City, PH: C & E Publishing.

Stillwell, J. “Mathematics and History 3rd Edition”, Springer, United States of America, 2010.

Taha, H. A. (2007). Operations research: An introduction [PDF]. Retrieved from <http://www.math.upatras.gr/~tsantas/DownLoadFiles/Taha%20-%20Operation%20Research%208Ed.pdf>.

Turban, E. & Meredith, J. R. (n.d.) Fundamentals of management science [PDF]. Retrieved from <https://openlibrary.org/books/OL4579281M/Fundamentals_of_management_science>.

Victoriano, P. S. (1990). Quantitative techniques for business management. Manila, PH: Rex Bookstore.

Course Outline

Introduction
Mathematics in Our World
- History of Mathematics and Its Major Players
- Mathematics and the Search for Truth and Understanding
Patterns in Nature and Regularities in the World
- Occurrence of Sequences in Nature
- Fractions as It Occurs in Nature
- The Phi Ratio and Its Evidence in Nature
- Symmetry in Nature, Mathematics in Music and in Architecture
Mathematical Language and Symbols
- Set and Set Operations
- Set of Real Numbers, Its Properties and Operations
- Venn Diagrams
- Application of Venn Diagrams in Relation to the Sets
Data Management
- Descriptive statistics: Measures of central tendency, variation, and relative standing
- Inferential statistics: Normal distribution, correlation, linear regression and hypothesis testing
Logic
- Logic Statements, Logical Connectives
- Truth Values and Truth Tables
- Condition and Related Statements, Bi-conditional Statements
- Tautologies and Contradictions
Logic and Arguments
- Open Sentence and Quantifiers
- Symbolic Arguments and Its Validity
- Arguments and Venn (Euler) Diagrams
Application of Symbolic Logic: Switching Networks
Mathematical Proofs
- Direct Proof
- Indirect Proof
- Methods of Disproof
- Principle of Mathematical Induction
Mathematics of Graphs
- Graphs, Paths and Circuits
- Weighted Graphs and Its Application
- Subgraph and Planarity of Graphs
- Chromatic Number and Its Application to Scheduling
- Modeling Traffic Lights with Graphs
Linear Programming in Two Variables
- Formulation of the Objective Functions and Constraints
- Solution by the Graphical Method and the Simplex Method
The Mathematics of Finance
- Annuity
- How individual taxes are computed
- Inheritance: Fair Division Procedures Using Mathematics
Weighted Voting Systems
- How Weighted Voting Works
- Mathematical Notation for Weighted Voting
- The Banzhaf Power Index
- Computing the Power Index
- Finding the Weights
- Veto Power: A Probabilistic Interpretation
- A Pictorial View of Weighted Voting
- Applying the Banzhaf Index
Fair Division and Apportionment
- The Continuous Case: Two Players and Multiple Players
- The Discrete Case: Two Players and Multiple Players
- Political Apportionment
- Apportionment Methods
- Hamilton's Method
- Divisor Methods
- An Application to Scheduling
- Undesirable Outcomes

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