The broad spectrum of Mathematics Jomar Fajardo Rabajante, Dr.Sc. jfrabajante@up.edu.ph
Outline Mathematics Applied Mathematics Application area Numeracy
systematic ^ study of patterns ^ based on logic deductive What is Mathematics? systematic ^ study of patterns ^ based on logic deductive
Applied Pure Mathematics Algebra Geometry Analysis Modeling Algorithm & Simulation
Branches of Mathematics Pure Algebra Geometry Analysis Applied Modeling Algorithm & Simulation “Study of objects and operations: structures”
Branches of Mathematics Pure Algebra Geometry Analysis Applied Modeling Algorithm & Simulation “Study of shapes and spaces”
Branches of Mathematics Pure Algebra Geometry Analysis Applied Modeling Algorithm & Simulation “Study of limits and change”
Branches of Mathematics Pure Algebra Geometry Analysis Applied Modeling Algorithm & Simulation Number theory Combinatorics etc…
Branches of Mathematics Pure Algebra Geometry Analysis Applied Modeling Algorithm & Simulation Foundations (e.g., Logic and Set theory)
Branches of Mathematics “Translate to mathematical language” Pure Algebra Geometry Analysis Applied Modeling Algorithm & Simulation
Branches of Mathematics Pure Algebra Geometry Analysis Applied Modeling Algorithm & Simulation “Analyze and solve”
APPLIED MATHEMATICS CORE Theories in Mathematics: >Brain< Math modeling: >Heart< Methods and algorithms: >Arms< Application areas: >Legs<
GOAL! + domain of application So what is the difference between theoretical (pure) and applied mathematics? GOAL! + domain of application
APPLIED MATHEMATICS Pure Math Application area Applied Math
Theoretical Math Application area Applied Math APPLIED MATHEMATICS There are no distinct boundaries Applied Math
PURE/THEORETICAL MATHEMATICS Domain 1 Domain 2 Domain 3 Domain 4 Domain 5 A P L I E D S P E C T R U M M A T H PURE/THEORETICAL MATHEMATICS
PURE/THEORETICAL MATHEMATICS Domain 1 Domain 2 Domain 3 Domain 4 Domain 5 Mathematical [Biology, Physics, Chemistry, Social Science, Economics…] Engineering Mathematics Statistics Computational Science A P L I E D S P E C T R U M M A T H PURE/THEORETICAL MATHEMATICS
PURE/THEORETICAL MATHEMATICS Domain 1 Domain 2 Domain 3 Domain 4 Domain 5 Collaboration! A P L I E D S P E C T R U M M A T H PURE/THEORETICAL MATHEMATICS
PURE/THEORETICAL MATHEMATICS Domain 1 Domain 2 Domain 3 Domain 4 Domain 5 PURE/THEORETICAL MATHEMATICS
PURE/THEORETICAL MATHEMATICS Domain 1 Domain 2 Domain 3 Domain 4 Domain 5 PURE/THEORETICAL MATHEMATICS
THEORETICAL MATHEMATICS Domain 1 Domain 2 Domain 3 Domain 4 Domain 5 A P L I E D S P E C T R U M M A T H THEORETICAL MATHEMATICS
What is science? Formal Sciences Natural Sciences (physical sciences and life sciences) Social Sciences
Aristotle: Deductive Logic (384– 322 BC) HISTORY Aristotle: Deductive Logic (384– 322 BC)
Francis Bacon: Induction Or Confirmation (1561– 1626) HISTORY Francis Bacon: Induction Or Confirmation (1561– 1626)
Karl Popper: Falsification (1902–1994) HISTORY Karl Popper: Falsification (1902–1994)
Marriage of Deductive and Inductive Logic demarcation of science from non-science (fringe science, pseudoscience and junk science)
Thomas Kuhn: Paradigm (1922–1996) HISTORY Thomas Kuhn: Paradigm (1922–1996)
MATH MODELING PROCESS Follows the Scientific Method Must adhere to the Philosophy of Science: >Falsifiability<
MATH MODELING PROCESS
EXAMPLE 1 force of gravity arises from the curvature of space-time Solar eclipse of May 29, 1919 force of gravity arises from the curvature of space-time The case of Mercury
EXAMPLE 1 force of gravity arises from the curvature of space-time 12 June 2017
EXAMPLE 1
EXAMPLE 2
EXAMPLE 2
EXAMPLE 2 MacArthur et al., PLoS ONE, 2008
EXAMPLE 2 MacArthur et al., PLoS ONE, 2008
EXAMPLE 2
EXAMPLE 3 http://www.nature.com/articles/srep10004
EXAMPLE 3 http://advances.sciencemag.org/content/2/3/e1501548
EXAMPLE 3 1 “Killing the Winner” hypothesis 1
EXAMPLE 3
EXAMPLE 3 Red Queen in Nature
EXAMPLE 3 Red Queen in Nature
EXAMPLE 3 Red Queen in Nature
EXAMPLE 3 >85% Testable Hypothesis
EXAMPLE 3 Testable Hypothesis
EXAMPLE 3
For all Filipinos! Numeracy “mathematical thinking” without taking a math degree experts
Quantitative Literacy/Numeracy ability to use mathematics in everyday life
INDUSTRY 4.0 Increasing challenge The digital age puts a new premium on numeracy skills than ever before. Computers can do the maths for us, but we need good numeracy in order to use them effectively.
My advocacies National roadmap for applied mathematics (to increase impact and make it intentionally socially relevant) Mathematics and scientific thinking for all Filipinos (e.g., survey criteria)
My story
My story