1. The broad spectrum of Mathematics
Jomar Fajardo Rabajante, Dr.Sc.

2. Outline
Mathematics
Applied Mathematics
Application area
Numeracy

3. systematic ^ study of patterns ^ based on logic deductive
What is Mathematics?
systematic ^
study of patterns ^
based on logic
deductive

4. Applied Pure Mathematics Algebra Geometry Analysis Modeling
Algorithm & Simulation

5. Branches of Mathematics
Pure
Algebra
Geometry
Analysis
Applied
Modeling
Algorithm & Simulation
“Study of objects and operations: structures”

6. Branches of Mathematics
Pure
Algebra
Geometry
Analysis
Applied
Modeling
Algorithm & Simulation
“Study of shapes and spaces”

7. Branches of Mathematics
Pure
Algebra
Geometry
Analysis
Applied
Modeling
Algorithm & Simulation
“Study of limits and change”

8. Branches of Mathematics
Pure
Algebra
Geometry
Analysis
Applied
Modeling
Algorithm & Simulation
Number theory
Combinatorics
etc…

9. Branches of Mathematics
Pure
Algebra
Geometry
Analysis
Applied
Modeling
Algorithm & Simulation
Foundations (e.g., Logic and Set theory)

10. Branches of Mathematics
“Translate to mathematical language”
Pure
Algebra
Geometry
Analysis
Applied
Modeling
Algorithm & Simulation

11. Branches of Mathematics
Pure
Algebra
Geometry
Analysis
Applied
Modeling
Algorithm & Simulation
“Analyze and solve”

12. APPLIED MATHEMATICS CORE
Theories in Mathematics: >Brain<
Math modeling: >Heart<
Methods and algorithms: >Arms<
Application areas: >Legs<

13. GOAL! + domain of application
So what is the difference between theoretical (pure) and applied mathematics?
GOAL! +
domain of application

14. APPLIED MATHEMATICS
Pure
Math
Application
area
Applied Math

15. Theoretical Math Application area Applied Math APPLIED MATHEMATICS
There are no distinct boundaries
Applied Math

16. 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

17. 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

18. 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

19. PURE/THEORETICAL MATHEMATICS
Domain 1
Domain 2
Domain 3
Domain 4
Domain 5
PURE/THEORETICAL MATHEMATICS

20. PURE/THEORETICAL MATHEMATICS
Domain 1
Domain 2
Domain 3
Domain 4
Domain 5
PURE/THEORETICAL MATHEMATICS

22. 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

23. What is science? Formal Sciences
Natural Sciences (physical sciences and life sciences)
Social Sciences

24. Aristotle: Deductive Logic (384– 322 BC)
HISTORY
Aristotle: Deductive Logic
(384– 322 BC)

25. Francis Bacon: Induction Or Confirmation (1561– 1626)
HISTORY
Francis Bacon: Induction Or Confirmation (1561– 1626)

26. Karl Popper: Falsification (1902–1994)
HISTORY
Karl Popper: Falsification (1902–1994)

27. Marriage of Deductive and Inductive Logic
demarcation of science from non-science (fringe science, pseudoscience and junk science)

28. Thomas Kuhn: Paradigm (1922–1996)
HISTORY
Thomas Kuhn: Paradigm (1922–1996)

29. MATH MODELING PROCESS Follows the Scientific Method
Must adhere to the Philosophy of Science: >Falsifiability<

30. MATH MODELING PROCESS

31. 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

32. EXAMPLE 1 force of gravity arises from the curvature of space-time
12 June 2017

33. EXAMPLE 1

34. EXAMPLE 2

35. EXAMPLE 2

36. EXAMPLE 2
MacArthur et al., PLoS ONE, 2008

37. EXAMPLE 2
MacArthur et al., PLoS ONE, 2008

38. EXAMPLE 2

39. EXAMPLE 3

40. EXAMPLE 3

41. EXAMPLE 3 1
“Killing the Winner”
hypothesis 1

42. EXAMPLE 3

43. EXAMPLE 3
Red Queen in Nature

44. EXAMPLE 3
Red Queen in Nature

45. EXAMPLE 3
Red Queen in Nature

46. EXAMPLE 3
>85%
Testable Hypothesis

47. EXAMPLE 3
Testable Hypothesis

48. EXAMPLE 3

49. For all Filipinos! Numeracy
“mathematical thinking” without taking a math degree
experts

50. Quantitative Literacy/Numeracy
ability to use mathematics in everyday life

51. 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.

52. 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)

53. My story

54. My story