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Abstract algebra

Note Taking Guide 1.1

Subject: 
Algebra
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Elementary arithmetic
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Integers
Subtraction
Division
Multiplication
Number

Numerical Operations Essential Questions After completing this lesson, you will be able to answer the following questions: How are expressions rewritten in simplified form based on the mathematical operations in the expression? What is the correct order for performing mathematical operations in simplifying expressions? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Real Numbers(P.1) Natural Number: _______________ integers ____________ Numbers: A member of the set of positive integers or zero Integers: A number that can be written without a fraction or _______________ Rational Numbers: Can include positive/negative fractions and decimals. Irrational Number: Any real number that can not be expressed as a ratio. Adding and Subtracting Integers(P.2)

Polynomials

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Algebra
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Polynomials
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Abstract algebra
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By now, you should be familiar with variables and exponents, and you may have dealt with expressions like 3x4 or 6x. Polynomials are sums of these "variables and exponents" expressions. Each piece of the polynomial, each part that is being added, is called a "term". Polynomial terms have variables which are raised to whole-number exponents (or else the terms are just plain numbers); there are no square roots of variables, no fractional powers, and no variables in the denominator of any fractions. Here are some examples:Notice the exponents on the terms. The first term has an exponent of 2; the second term has an "understood" exponent of 1; and the last term doesn't have any variable at all.

Algebra 2

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Algebra
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General topology
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Constructible universe
Closed set
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. A subset of the real numbers is closed under addition if, for any two numbers, a and b, that are members of the subset, the number is also a member of the subset. Tell whether each of the following subsets of the real numbers is closed under addition. If it is not, give an example that shows it is not. a. The set of whole numbers b. The set of negative integers c. The set of irrational numbers d. The set of rational numbers 2. For each of the sets in Problem 1, tell whether the set is closed under multiplication. If it is not, give an example that shows it is not. 3. a. For each of the following pairs of rational numbers, and find the rational number and write the 3 rational numbers in increasing order. (i) (ii) (iii) (iv)

Inverse Hyperbolic Functions

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Trigonometry
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Inverse function
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Logarithm
Exponential function
Exponentiation

Since hyperbolic functions are defined in terms of exponential functions, it is expected that their inverses can be expressed in the inverse of their exponential functions: Inverse Hyperbolic Functions in terms of logarithms 

7inver1,7inver2,7inver3,7inver4,7inver5,7inver6,7inver7,7inver8,7inver9,7inver10,7inver11,7inver12



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