By P. J. Hilton;S. Wylie
This account of algebraic topology is whole in itself, assuming no past wisdom of the topic. it really is used as a textbook for college students within the ultimate 12 months of an undergraduate direction or on graduate classes and as a instruction manual for mathematicians in different branches who wish a few wisdom of the topic.
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Extra resources for Homology Theory: An Introduction to Algebraic Topology
EXAMPLE 13 Distributive Property (a) 2 # 1x + 32 = 2 # x + 2 # 3 = 2x + 6 (b) 3x + 5x = 13 + 52x = 8x Use to remove parentheses. Use to combine two expressions. (c) 1x + 221x + 32 = x1x + 32 + 21x + 32 = 1x2 + 3x2 + 12x + 62 = x2 + (3x + 2x) + 6 = x2 + 5x + 6 Now Work PROBLEM ᭹ 87 The real numbers 0 and 1 have unique properties, called the identity properties. 1 Real Numbers 11 Identity Properties 0 + a = a + 0 = a a#1 = 1#a = a (4a) (4b) We call 0 the additive identity and 1 the multiplicative identity.
The product of 5 and 2 equals 10. 41. The sum of x and 2 is the product of 3 and 4. 42. The sum of 3 and y is the sum of 2 and 2. 43. The product of 3 and y is the sum of 1 and 2. 44. The product of 2 and x is the product of 4 and 6. 45. The difference x less 2 equals 6. 46. The difference 2 less y equals 6. 47. The quotient x divided by 2 is 6. 48. The quotient 2 divided by x is 6. In Problems 49–86, evaluate each expression. 49. 9 - 4 + 2 50. 6 - 4 + 3 51. -6 + 4 # 3 53. 4 + 5 - 8 54. 8 - 3 - 4 55.
What was his balance at the end of the month? In Problems 147 and 148, write an inequality using an absolute value to describe each statement. 147. x is at least 6 units from 4. 148. x is more than 5 units from 2. 149. S. Voltage In the United States, normal household voltage is 110 volts. It is acceptable for the actual voltage x to differ from normal by at most 5 volts. A formula that describes this is ƒ x - 110 ƒ … 5 (a) Show that a voltage of 108 volts is acceptable. (b) Show that a voltage of 104 volts is not acceptable.
Homology Theory: An Introduction to Algebraic Topology by P. J. Hilton;S. Wylie