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Data Abstraction: Rational Numbers
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Related lectures (31)
Dedekind Cuts: Rational Numbers
Explores Dedekind cuts in rational numbers, essential for constructing real numbers.
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Covers the basic concepts of rational numbers and algebraic operations, including addition, subtraction, multiplication, and division.
Complex Numbers: Introduction and Operations
Introduces complex numbers and their forms, including Cartesian, polar, and exponential forms, and explains how to find the argument of a complex number.
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Introduces real numbers, their properties, and their significance in analysis.
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Explains the properties of addition and multiplication in Q with illustrative examples.
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Explores the construction of rational numbers, irreducible fractions, equivalence, and simplification rules.
Decimal Expansion: Division and Periodicity
Delves into decimal expansion of rational numbers through Euclidean division, emphasizing periodicity and illustrative examples.
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Delves into infinite decimal numbers, exploring convergence and divergence, and showcasing examples of rational and irrational numbers.
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Covers the definition and operations involving rational numbers.
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Covers the concept of total order relation and properties of real numbers.
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Explores even squares, irrationality of √2, gaps in rational numbers, and minorants in Q.
Rational Numbers: Construction and Properties
Covers the construction and properties of rational numbers, including fractions and equivalence, with proofs on commutativity.
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Covers the concepts of infimum and supremum of subsets in real numbers.
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Explores boundaries in sets, defining them as points not well separated from the set or its complement.
Simplex: Implementation and Methods
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Covers the implementation of the Simplex algorithm and its methods.
Mathematical Notations: Recap and Rational Numbers
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Covers a recap on mathematical notations and introduces rational numbers and basic algebraic operations.
Introduction to Analysis
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Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.
Complex Numbers: Algebraic Structures and Applications
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Covers algebraic structures, real numbers, fields, and the applications of complex numbers in science and engineering.
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