Download e-book for iPad: Discrete Mathematics: An Open Introduction by Oscar Levin

By Oscar Levin

ISBN-10: 1534970746

ISBN-13: 9781534970748

Note, this is often the corrected Fall 2015 variation. a brand new version can be on hand August 2016

This light creation to discrete arithmetic is written for first and moment 12 months math majors, specially those that intend to educate. The textual content started as a collection of lecture notes for the discrete arithmetic path on the collage of Northern Colorado. This path serves either as an advent to issues in discrete math and because the "introduction to facts" direction for math majors. The direction is generally taught with a large number of scholar inquiry, and this article is written to aid facilitate this.

Four major issues are coated: counting, sequences, good judgment, and graph thought. alongside the way in which proofs are brought, together with proofs through contradiction, proofs via induction, and combinatorial proofs. The e-book includes 299 routines, all with strategies (or at the very least a hint), in addition to forty five extra extra concerned difficulties compatible for homework. There also are Investigate! difficulties in the course of the textual content to help lively, inquiry dependent learning.

While there are numerous nice discrete math textbooks on hand, this article has the subsequent benefits:

  • it truly is written for use in an inquiry wealthy course.
  • It is written for use in a path for destiny math teachers.
  • it really is open resource, with comparatively cheap print variants and unfastened digital editions.

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Additional info for Discrete Mathematics: An Open Introduction

Example text

For your college interview, you must wear a tie. You own 3 regular (boring) ties and 5 (cool) bow ties. (a) How many choices do you have for your neck-wear? (b) You realize that the interview is for clown college, so you should probably wear both a regular tie and a bow tie. How many choices do you have now? (c) For the rest of your outfit, you have 5 shirts, 4 skirts, 3 pants, and 7 dresses. You want to select either a shirt to wear with a skirt or pants, or just a dress. How many outfits do you have to choose from?

D) Find f −1 (0). (e) Find f −1 (12). 7. Let A { n ∈ N : 0 ≤ n ≤ 999} be the set of all numbers with three or fewer digits. Define the function f : A → N by f ( abc ) a + b + c, where a, b, and c are the digits of the number in A. For example, f (253) 2 + 5 + 3 10. (a) Find f −1 (3). (b) Find f −1 (28). (c) Is f injective. Explain. (d) Is f surjective. Explain. 8. Let f : X → Y be some function. Suppose 3 ∈ Y. What can you say about f −1 (3) if you know, (a) f is injective? Explain. (b) f is surjective?

Not surprisingly then, the formula for cardinality of the union of three non-disjoint sets is more complicated: Cardinality of a union (3 sets) For any finite sets A, B, and C, |A ∪ B ∪ C | |A| + |B | + |C | − |A ∩ B | − |A ∩ C | − |B ∩ C | + |A ∩ B ∩ C | To determine how many elements are in at least one of A, B, or C we add up all the elements in each of those sets. However, when we do that, any element in both A and B is counted twice. Also, each element in both A and C is counted twice, as are elements in B and C, so we take each of those out of our sum once.

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Discrete Mathematics: An Open Introduction by Oscar Levin

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