Podcast
Questions and Answers
Which area of study includes quantity, structure, space, and change?
Which area of study includes quantity, structure, space, and change?
- Literature
- Biology
- Mathematics (correct)
- History
Which branch of mathematics deals with numbers, their actions, and generalizations?
Which branch of mathematics deals with numbers, their actions, and generalizations?
- Quantity (correct)
- Calculus
- Topology
- Geometry
Which field was developed to clarify the foundations of mathematics?
Which field was developed to clarify the foundations of mathematics?
- Astrology
- Linguistics
- Mathematical Logic (correct)
- Chemistry
What are statements proven on the basis of previously established statements called?
What are statements proven on the basis of previously established statements called?
Which type of mathematics explores concepts without regard to applications outside of mathematics?
Which type of mathematics explores concepts without regard to applications outside of mathematics?
What is applied mathematics concerned with?
What is applied mathematics concerned with?
In which fields are mathematical models widely used?
In which fields are mathematical models widely used?
What is directly useful in data analysis, allowing researchers to test hypotheses?
What is directly useful in data analysis, allowing researchers to test hypotheses?
What is a widespread convention for formulas in mathematical journals and books?
What is a widespread convention for formulas in mathematical journals and books?
Which of the following describes mathematical notation?
Which of the following describes mathematical notation?
Flashcards
What is mathematics?
What is mathematics?
The study of quantity, structure, space, and change.
Mathematical logic
Mathematical logic
Deals with applying formal logic to mathematics.
Mathematical notation
Mathematical notation
Uses symbols to represent mathematical objects and concepts.
What is a theorem?
What is a theorem?
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Pure mathematics
Pure mathematics
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Applied mathematics
Applied mathematics
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Mathematics in science
Mathematics in science
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Statistics
Statistics
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Mathematical models in science
Mathematical models in science
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Beauty in mathematics
Beauty in mathematics
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Study Notes
- Math is the study of topics such as quantity, structure, space, and change
- There are different views among mathematicians and philosophers as to the exact scope and definition of mathematics
History
- The history of mathematics can be divided into distinct periods - Mesopotamia, Egypt, Ancient Greece, Hellenistic mathematics, Islamic mathematics, India, Renaissance, and 19th century mathematics
- Mathematical discoveries continue to be made today
Branches
- Quantity relates to numbers, describing their actions, and investigating their generalizations
- Structure relates to mathematical objects and their relationships to each other
- Space originates from the representation of the world around us
- Change is perhaps the most self-evident category and is handled by calculus
Foundations and Philosophy
- To clarify the foundations of mathematics, the fields of mathematical logic and set theory were developed
- Mathematical logic deals with applying formal logic to mathematics
Notation, Terminology, and Style
- Mathematical notation has ramified greatly over time
- Mathematical notation uses symbols to represent mathematical objects and concepts
- A theorem is a statement that has been proven on the basis of previously established statements
- According to a widespread convention, articles appearing in mathematical journals and books are generally based on a style in which all formulas have been rendered in italics
Pure and Applied Mathematics
- Pure mathematics explores mathematical concepts without regard to applications outside of mathematics
- Applied mathematics is concerned with the use of mathematical tools to solve problems in science, engineering, and other fields
Relationship with Science
- Mathematics is essential to many fields of science, both theoretical and applied
- Mathematical models are widely used in physics, chemistry, biology, and other disciplines
- Statistics is directly useful in data analysis, allowing researchers to test hypotheses and draw conclusions from empirical data
Beauty
- Many mathematicians are drawn to their subject for its beauty
- One aspect of beauty is its precision
- There are many philosophical debates about mathematics and its impact on society
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