Thinking Mathematically

Jul 17, 2024

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Dive into the world of mathematics and learn to think analytically, solve problems, and make informed decisions using numerical data. This comprehensive guide will equip you with the tools to approach mathematical challenges with confidence and clarity. Whether you're a student, educator, or enthusiast, this book will enhance your mathematical reasoning skills and help you unlock new possibilities through the power of logical thinking.

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Thinking Mathematically

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Thinking Mathematically

Thinking Mathematically. Arithmetic and Geometric Sequences. 8. 2. 5. 3. 1. 1. a 3 =. a 4 =. a 6 =. a 5 =. a 1. a 2. a 3 + a 4. a 1 + a 2. a 4 + a 5. a 2 + a 3. “Sequences”.

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Thinking Mathematically

Thinking Mathematically. Statistics: 12.1 Sampling, Frequency Distributions, and Graphs. Statistics. Statistics is the science of data. This involves collecting, organizing, analyzing, and interpreting numerical information, as well as drawing conclusions based on the data.

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Thinking Mathematically

Number Representation and Calculation 4.1 Our Hindu-Arabic System and Early Positional Systems. Thinking Mathematically. “Exponential” Notation. An “exponent” is a small number written slightly above and just to the right of a number or an expression .

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Thinking Mathematically

Thinking Mathematically. Counting Methods and Probability 11.1 The Fundamental Counting Principle. The Fundamental Counting Principle. If you can choose one item from a group of M items and a second item from a group of N items, then the total number of two-item choices is M  N.

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Thinking Mathematically

Thinking Mathematically. Combinations. A combination of items occurs when:. The item are selected from the same group. No item is used more than once. The order of the items makes no difference. Example Distinguishing between Permutations and Combinations.

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Thinking Mathematically

Thinking Mathematically. Permutations. Permutations. No item is used more than once. The order of arrangement makes a difference. Example Counting Permutations.

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Thinking Mathematically

Thinking Mathematically. Events Involving Not and Or; Odds. The Probability of an Event Not Occurring. The probability that an event E will not occur is equal to one minus the probability that it will occur. P(not E) = 1 - P(E). Example The Probability of an Event Not Occurring.

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Thinking Mathematically

Thinking Mathematically. Algebra: Equations and Inequalities 6.6 Solving Quadratic Equations. Definition of a Quadratic Equation. A quadratic equation in x is an equation that can be written in the general form ax 2 + bx + c = 0, where a, b, and c are real numbers, with a ≠0 .

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Thinking Mathematically

Thinking Mathematically. Probability with the Fundamental Counting Principle, Permutations, and Combinations. Example Probability and Permutations.

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Thinking Mathematically

Chapter 2 Set Theory 2.1 Basic Set Concepts. Thinking Mathematically. Basic Set Concepts. A set is a collection of objects. Each object is called an element of the set. A set must be well defined : Its contents can be clearly determined

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Thinking Mathematically

Thinking Mathematically. Logic 3.2 Compound Statements and Connectives. “Compound” Statements. Simple statements can be connected with “and”, “Either … or”, “If … then”, or “if and only if.” These more complicated statements are called “compound.”. Symbolic Logic. Symbolic Logic (cont.).

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Thinking Mathematically

Thinking Mathematically. Logic 3.1 Statements, Negations, and Quantified Statements. Statements. A “statement” is a sentence that is either “true” or “false” but not both at the same time. Exercise Set 3.1 #3, 9 Statement? On January 20, 2009, John McCain became America’s 44 th president.

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Thinking Mathematically

Thinking Mathematically. Linear Programming. Example Writing an Objective Function.

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Thinking Mathematically

Thinking Mathematically. Estimation and Graphs. Estimation. The process of getting an approximate answer to a question. Different situations require varying degrees of accuracy. Examples: Giving a tip, buying enough beer for a party, or what you need on the final to get an A in a course.

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Thinking Mathematically

Thinking Mathematically. The Cost of Home Ownership. Terminology. Mortgage broker - offers to find you a mortgage lender willing to make you a loan. Fixed rate mortgage - have the same monthly payment during the entire time of the loan

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Thinking Mathematically

Thinking Mathematically. Chapter 11: Counting Methods and Probability Theory. Thinking Mathematically. Section 1: The Fundamental Counting Principle. The Fundamental Counting Principle.

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Thinking Mathematically

Thinking Mathematically. Volume. Volume of Boxlike Shapes: V = lwh. Volume of a Pyramid: V = (1/3)Bh where B is the area of the base. Volume of a Right Circular Cylinder: V =  r 2 h. Example Finding the Volume of a Cylinder.

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Thinking Mathematically

Number Theory and the Real Number System 5.1 Prime and Composite Numbers. Thinking Mathematically. The Set of Natural Numbers. N = {1,2,3,4,5,6,7, 8, 9, 10, 11, ... }. Divisibility.

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Thinking Mathematically

Thinking Mathematically. Problem Solving and Critical Thinking. Example. You purchased textbooks for 4 classes. Each book cost more than $50.00. Inductive Reasoning. “Inductive reasoning” is the process of arriving at a general conclusion based on observations of specific examples.

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Thinking Mathematically

Thinking Mathematically. Number Theory: Prime and Composite Numbers. The Set of Natural Numbers. N = {1,2,3,4,5,6,7, 8, 9, 10, 11, ... }. Divisibility.

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Thinking Mathematically

Thinking Mathematically. The Irrational Numbers. The Irrational Numbers. The set of irrational numbers is the set of number whose decimal representations are neither terminating nor repeating.

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