The document discusses the importance and nature of mathematics. It defines mathematics as the science of structure, order, and relations that has evolved from counting and measuring. Some key characteristics of mathematics include classification, logical sequence, structure, generalization, applicability, precision/accuracy, abstractness, symbolism. Mathematics is described as a science of measures, an intellectual game, an art of drawing conclusions, a tool subject, and a system of logical procedure. Examples are given of how mathematics is applied in various fields like nature, medicine, engineering. Famous mathematicians like Pythagoras, Einstein, Descartes, Marie Curie, Kepler, Euclid, and Leonardo Pisano are also mentioned.

1. By:
Arlene M. Leron

3. Objectives:
At the end of the lesson, you should be able to
perform the following tasks:
1. Articulate the importance of mathematics in one’s
life.
2. Give the characteristics and nature of mathematics.
3. Express appreciation for mathematics as a human
endeavor.
4. Identify some famous mathematicians of all times
and their contribution in the field of mathematics.

4. What is Mathematics?
-Mathêma “that which is learnt” derived from
“manthano”, and modern Greek “mathaino”
which means “to learn”
- “The science of structure, order, and relations that
has evolved from elemental practices of counting,
measuring, and describing the shapes and
characteristics of objects”. (Encyclopedia
Britannica)

5. Characteristics
of
Mathematics
Classification
Logical
Sequence
Structure
Generalization
Applicability
Mathematical
language &
symbolism
Precision &
Accuracy
Abstractness

6. Classification
generates a series of
mental relations
through which objects
are grouped according
to similarities and
differences depending
on specific criteria
such as shape, color,
size, etc.
Characteristics of Mathematics

7. Logical Sequence -
ideas in mathematics
need to flow in an order
that makes sense. It
means that each step can
be derived logically from
the preceding steps.
Characteristics of Mathematics

8. Characteristics of Mathematics
Structure- the structure on a particular
mathematical set will allow mathematicians to
study the set further and find its relationship
with other objects.

9. Characteristics of
Mathematics
Precision and
Accuracy – Accuracy is
how close a measured
value is to the actual
(true) value. It is the
degree to which a given
quantity is correct and
free from error. Precision,
is how close the
measured valued values
are to each other.

10. Characteristics of Mathematics
Abstractness- is the process of extracting the
underlying essence of a mathematical concept by
taking away any dependence on real-world objects.

11. Characteristics of
Mathematics
Symbolism – This
language is uniquely
constructed in such a way
that all mathematicians
understand symbolic
notations and mathematical
formulas.

12. Characteristics of
Mathematics
Applicability- The
applicability of
mathematics can lie
anywhere on a spectrum
from the completely
simple (trivial) to the
utterly complex
(mysterious).

13. Characteristics of Mathematics
Generalizations – The process of finding and
singling out in a whole class of similar objects.

14. Nature of
Mathematics
A science of
measures
A tool subject
An intellectual
game
The art of
drawing
conclusions
An intuitive
method
A system of
logical
procedure

15. A science of
measures- it is an
activity that involves
interaction with a
concrete system with
the aim of
representing aspects
of that system in
abstract terms of
“concrete” implies
“real”.
Nature of Mathematics

16. Intellectual game-
mathematics requires
visual imagery. Games
and mathematics both
require a strong dose
of patience, restraint,
and concentration.
Nature of Mathematics

17. The art of drawing
conclusions- Being able
to reason is essential to
understanding
mathematics. Reasoning
is a way to use
mathematical knowledge
and to generate and
solidify new
mathematical ideas.
Nature of Mathematics

18. A tool subject –
mathematics undeniably
a highly powerful
instrument of
investigation.
Mathematics is applied
in the fields of
engineering, life
sciences, industry, and
business.
Nature of Mathematics

19. A system of logical
procedure – Problem
solving is a skill which
can enhance our logical
reasoning.
Nature of Mathematics

20. An intuitive method –
mathematics also
requires the use of
intuition, the ability to
see what is reasonable
or not and the ability to
pu all these together.
Nature of Mathematics

21. The Beauty
of
Mathematics

22. Mathematics
IN Nature

26. Mathematics
IN Medical
Field

28. Mathematics
IN Forensic

29. Mathematics
IN Fluid Dynamics

30. Mathematics
IN Information
technology

31. Mathematics
IN Archeology

32. Mathematics
IN Social
Sciences

33. Mathematics
IN Political
Sciences

34. Mathematics
IN Music and
ARTS

35. Some Famous Mathematicians of
Modern Time
Pythagoras

36. Some Famous Mathematicians of
Modern Time
Albert Einstein

37. Some Famous Mathematicians of
Modern Time
Rene Descartes

38. Some Famous Mathematicians of
Modern Time
Marie Curie

39. Some Famous Mathematicians of
Modern Time
Johannes Kepler

40. Some Famous Mathematicians of
Modern Time
Euclid

41. Some Famous Mathematicians of
Modern Time
Leonardo Pisano

42. “Those laws of nature are within the grasp
of the human mind; God wanted us to
recognize them by creating us after his own
image so that we could share his own
thoughts”
- Johannes Kepler