MAT 103 (Chapter 1 & 2) - Prof. Mace
What's the Four Step Problem Solving Process? (p. 3)
1. Understanding the problem 2. Devising a plan 3. Carrying out the plan 4. Looking back
Ratio (p. 26)
A fixed nonzero number
Recursive formula (p. 22)
A formula based on a recursive pattern
Exponent (p. 27)
A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression. (Ex: 2^2)
Fibonacci sequence (p. 26)
A sequence with 0 as a starting term. More typically, the sequence is seen as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. The sequence is not arithmetic as there is no fixed difference. The first two terms of the Fibonacci sequence are 1, 1 and each subsequent term is the sum of the previous two.
Figurate numbers (p. 28)
Based on geometrical patterns, provide examples of sequences that are neither arithmetic nor geometric.
Arithmetic sequence (p. 21)
Each successive term from the second term on is obtained from the previous term by the addition or subtraction of a fixed number.
Geometric sequence (p. 26)
Each successive term is obtained from its predecessor by multiplying by a fixed nonzero number. (Ex: 2, 4, 8, 16, 32,...)
Common difference (p. 21)
Obtained from the preceding term from by adding a fixed number
Recursive pattern (p. 21)
One or more consecutive terms are given to start, each successive term of the sequence is contained from the previous term(s).
Sequence (p. 21)
Ordered arrangement of numbers, figures, or objects. A sequence has items or terms identified as 1st, 2nd, 3rd, and so on. Sequence can be classified by their properties.
Counterexample (p. 19)
Proves the conjecture false.
nth term (p. 22)
Sometimes, rather than finding the next number in a linear sequence, you want to find the 41st number, or 110th number, say. Writing out 41 or 110 numbers takes a long time, so you can use a general rule. To find the value of any term in a sequence, use the nth term rule.
Conjectures (p. 19)
Statements or conclusions that have not be proven.
Gauss's Problem (p. 4)
Strategy that Carl Gauss came up with as a student to find the sum of the first 100 natural numbers. To understand the problem look at the natural numbers (ex: 1, 2, 3, 4,...), then find the sum 1 + 2 + 3 + 4 + ...... + 100.
Inductive reasoning (p. 19)
The method of making generalizations based on observations and patterns.
Deductive reasoning (p. 19)
The use of mathematical axioms, theorems, definitions, undefined terms assumed to be true, and logic for proof.
