A promenade in mathematical proofs: with comprenesive review of proof techniques
"Designed to support students as they advance their mathematical knowledge, bridging the gap from basic arithmetic and calculus to a deeper understanding of mathematical concepts through proof writing. It emphasizes the importance of being able to articulate mathematical ideas and solutions eff...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Solana Beach, CA
Cognella Academic Publishing
[2024]
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| Edition: | First edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "Designed to support students as they advance their mathematical knowledge, bridging the gap from basic arithmetic and calculus to a deeper understanding of mathematical concepts through proof writing. It emphasizes the importance of being able to articulate mathematical ideas and solutions effectively, asserting that proof writing is as crucial as the subject matter itself. The book is structured to build upon the reader's knowledge systematically, starting with mathematical writing and progressing through logic, set theory, proof techniques, and more advanced topics such as sequences, relations, and functions. Each chapter concludes with practice problems and solutions to reinforce learning."--Back cover |
| Physical Description: | 318 Seiten Illustrationen 28 cm |
| ISBN: | 9781793564283 1793564280 |
Staff View
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Record in the Search Index
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Il Contents 1 Preliminaries . . . . . . . . 11 1.1 Mathematical Writing 11 1.2 Identities 13 1.3 Absolute Values 13 1.4 Quadratic Functions and Equations 16 1.5 Chapter 1 Practice Problems 31 2 . . . . 35 2.1 Logic 35 2.2 Logical Connectives 37 2.3 Quantifiers 39 2.4 Implications 41 2.5 Bi-conditional Statements 42 2.6 2.7 Logical Equivalence Tautologies and Contradictions 42 45 2.8 Chapter 2 Practice Problems 47 2.9 Chapter 2 Additional Practice Problems with Solutions 50 3 SaIs 3.1 Introduction to Sets 55 3.2 Subsets 58 3.3 Power Sets 59 3.4 Set Operations 60 . 55
3.5 3.6 Complement 65 Indexed Sets and Partitions 68 3.7 3.8 The Cartesian Product Chapter 3 Practice Problems 71 74 3.9 Chapter 3 Additional Practice Problems with Solutions 77 ^3· Techniques of Proofs. 33 4.1 4.2 4.3 Direct Proofs 84 Proof by Contraposition Proof by Contradiction 101 104 4.4 Additional Proof Techniques 111 4.5 Mathematical Induction Proof 115 4.6 The Principle of Mathematical Induction 116 4.7 Strong Induction 122 4.8 Chapter 4 Practice Problems 129 4.9 Chapter 4 Additional Practice Problems with Solutions 133 More on Proof Techniques. 151 5.1 5.2 Examples from Sets 151 Examples from Calculus 159 5.3 5.4 Examples from Number Theory 164 172 5.5 5.7 More about Sums Examples from Linear Algebra Chapter 5 Practice Problems 190 5.8 Chapter 5 Additional Practice Problems with Solutions 192 Μ Sequences. 6.1 Sequences 199 6.2 Variations 201 6.3 Bounded Sequence 203 6.4 6.5 Convergence and Divergence Arithmetic Progression 204 211 6.6 6.7 Geometric Progression 217 Fibonacci Sequence 226 6.8 Adjacent Sequences 232 6.9 Chapter 6 Practice Problems 233 6.10 Chapter 6 Additional Practice Problems with Solutions 237 / Relations. 257 7.1 7.2 Relations Properties of Relations 5.6 Integer Part 177 187 . . 199 257 259
7.3 Equivalence Classes 261 7.4 Relations Between Sets 264 7.5 7.6 Chapter 7 Practice Problems Chapter 7 Additional Practice Problems with Solutions 266 267 d Functions . . 8.1 8.2 Functions 8.3 8.4 8.6 Composition Inverse Functions Image and Pre-image of a Set Cardinality of Sets 282 284 287 8.7 Chapter 8 Practice Problems 298 8.8 Chapter 8 Additional Practice Problems with Solutions 300 8.5 . 273 273 274 Injective, Surjective, and Bijective Functions Bibliography Index 279 . 7 ; |
| any_adam_object | 1 |
| author | Hamdi, Abdelouahed ca. 20./21. Jh |
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| id | DE-604.BV049918597 |
| illustrated | Illustrated |
| indexdate | 2025-02-12T07:00:55Z |
| institution | BVB |
| isbn | 9781793564283 1793564280 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035257240 |
| oclc_num | 1424456088 |
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| owner | DE-739 |
| owner_facet | DE-739 |
| physical | 318 Seiten Illustrationen 28 cm |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Cognella Academic Publishing |
| record_format | marc |
| spelling | Hamdi, Abdelouahed ca. 20./21. Jh. Verfasser (DE-588)1355127882 aut A promenade in mathematical proofs with comprenesive review of proof techniques Abdelouahed Hamdi and Noureen A. Khan First edition Solana Beach, CA Cognella Academic Publishing [2024] 318 Seiten Illustrationen 28 cm txt rdacontent n rdamedia nc rdacarrier "Designed to support students as they advance their mathematical knowledge, bridging the gap from basic arithmetic and calculus to a deeper understanding of mathematical concepts through proof writing. It emphasizes the importance of being able to articulate mathematical ideas and solutions effectively, asserting that proof writing is as crucial as the subject matter itself. The book is structured to build upon the reader's knowledge systematically, starting with mathematical writing and progressing through logic, set theory, proof techniques, and more advanced topics such as sequences, relations, and functions. Each chapter concludes with practice problems and solutions to reinforce learning."--Back cover Formaler Beweis (DE-588)4506115-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Proof theory / Textbooks Logic, Symbolic and mathematical / Textbooks Formaler Beweis (DE-588)4506115-4 s Mathematik (DE-588)4037944-9 s DE-604 Khan, Noureen ca. 20./21. Jh. Sonstige (DE-588)1355128129 oth Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035257240&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hamdi, Abdelouahed ca. 20./21. Jh A promenade in mathematical proofs with comprenesive review of proof techniques Formaler Beweis (DE-588)4506115-4 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4506115-4 (DE-588)4037944-9 |
| title | A promenade in mathematical proofs with comprenesive review of proof techniques |
| title_auth | A promenade in mathematical proofs with comprenesive review of proof techniques |
| title_exact_search | A promenade in mathematical proofs with comprenesive review of proof techniques |
| title_full | A promenade in mathematical proofs with comprenesive review of proof techniques Abdelouahed Hamdi and Noureen A. Khan |
| title_fullStr | A promenade in mathematical proofs with comprenesive review of proof techniques Abdelouahed Hamdi and Noureen A. Khan |
| title_full_unstemmed | A promenade in mathematical proofs with comprenesive review of proof techniques Abdelouahed Hamdi and Noureen A. Khan |
| title_short | A promenade in mathematical proofs |
| title_sort | a promenade in mathematical proofs with comprenesive review of proof techniques |
| title_sub | with comprenesive review of proof techniques |
| topic | Formaler Beweis (DE-588)4506115-4 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Formaler Beweis Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035257240&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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