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MTE1501Assignment 3
2023 (213891)
UPDATED
QUESTIONS AND
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ANSWERS
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, 3.1 LU1: MATHEMATICS IN SOCIETY
Read section 1.3: Defining Mathematics - in your study guide and provide the
differences between the three views used to outline the mathematics
consideration. (10)
In the context of defining mathematics, there are three broad perspectives or views that
mathematicians and philosophers often discuss: the Platonist view, the Formalist view,
and the Constructivist view. These views offer different interpretations of the nature and
existence of mathematical objects and the foundations of mathematics. Here's a brief
explanation of each view:
1. Platonist View: The Platonist view is based on the philosophy of Plato, who argued that
mathematical objects have an independent existence in an abstract realm of ideas or
forms. According to this view, mathematical objects and truths are discovered rather
than invented by humans. Platonists believe that mathematics is a universal and timeless
discipline, and mathematical objects exist regardless of whether humans conceive them.
2. Formalist View: The Formalist view, championed by mathematician David Hilbert,
focuses on the manipulation of symbols and formal systems. According to formalism,
mathematics is purely a game of manipulating symbols according to certain rules
without any necessary reference to external reality or meaning. In this view,
mathematical objects are considered to be mere formal constructs or patterns of
symbols.
3. Constructivist View: The Constructivist view, associated with mathematicians such as
L.E.J. Brouwer, emphasizes the role of human construction and intuition in mathematics.
Constructivists argue that mathematical objects and truths are products of human
mental activity and cannot exist independently of human thought. According to this
view, mathematical knowledge is actively constructed by mathematicians through the
process of intuition and logical reasoning.
These three views provide different perspectives on the nature of mathematics and the
way mathematical knowledge is obtained. It's important to note that these views
represent broad philosophical stances, and there are variations and nuances within each
perspective. Mathematicians and philosophers continue to explore and debate these
ideas to further our understanding of mathematics.
3.2 LU2: TEACHING AND LEARNING MATHEMATICS
3.2.1 Do activities: 3.5 a. 6 b. 8 c. 14 (5)
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