The broad spectrum of Mathematics

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Presentation transcript:

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