Computer Mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Ashland :
Arcler Press,
2019.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 1 online resource (268 pages) |
| ISBN: | 1773615971 9781773615974 |
Internformat
MARC
| LEADER | 00000cam a2200000Mu 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-on1085219852 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr |n|---||||| | ||
| 008 | 190209s2019 xx o 000 0 eng d | ||
| 040 | |a EBLCP |b eng |e pn |c EBLCP |d YDX |d OCLCQ |d UKAHL |d N$T |d OCLCO |d N$T |d OCLCF |d OCLCO |d K6U |d OCLCQ |d OCLCO |d OCLCL | ||
| 019 | |a 1084502391 |a 1084694062 |a 1284938266 | ||
| 020 | |a 1773615971 | ||
| 020 | |a 9781773615974 |q (electronic bk.) | ||
| 035 | |a (OCoLC)1085219852 |z (OCoLC)1084502391 |z (OCoLC)1084694062 |z (OCoLC)1284938266 | ||
| 050 | 4 | |a QA76.9.M35 | |
| 082 | 7 | |a 004.0151 |2 23 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Prudhomme, Gerard. | |
| 245 | 1 | 0 | |a Computer Mathematics |
| 260 | |a Ashland : |b Arcler Press, |c 2019. | ||
| 300 | |a 1 online resource (268 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover; Half Title Page; Title Page; Copyright Page; About the Author; Table of Contents; List of Figures; Preface; Chapter 1 Preparatory Mathematical and Computer Science Studies; Chapter 2 Predictable Phenomena; 2.1. Intensive Preliminary Courses of Logic; Chapter 3 Theory of Models and of Groups; Chapter 4 Programming Models; Chapter 5 Introduction to Formal Computer-Aided Proof; Chapter 6 Theory of the Demonstration; 6.1. Calculability And Incompleteness; Chapter 7 Working Group on Core Courses; 7.1. Verifications; 7.2. Complexity; Chapter 8 Finite Model Theory | |
| 505 | 8 | |a Chapter 9 Calculability and IncompletenessChapter 10 Programming Models; Chapter 11 Combinators; Chapter 12 Mathematical Logic; Chapter 13 Foundations of Computing; Chapter 14 Formal Arithmetic; Chapter 15 Database Object Component; Chapter 16 Arithmetization of Logic; Chapter 17 Computability and Complexity; Chapter 18 Polarization and Classical Logic; Chapter 19 Syntax and Semantics; Chapter 20 Proofs and Types; Chapter 21 Foundations for Programming Languages; 21.1. Basic Set Theory; Chapter 22 Descriptive Set Theory; 22.1. Structures And Techniques | |
| 505 | 8 | |a Chapter 23 Semantics of Programming LanguagesChapter 24 Stable Groups; Chapter 25 General Theory of Algorithms; Chapter 26 Recursive Functions; 26.1. Machine-Calculable Functions; Chapter 27 Logical Characterization of Computable Functions; Chapter 28 Notions of Reduction and Undecidable Problems; Chapter 29 Introduction to Complexity; Chapter 30 Theory of Finite Models and Applications; Chapter 31 Approximate Verification and Complexity; Chapter 32 Working on Fundamental Courses; Chapter 33 Preliminary Intensive Logic; Chapter 34 Classic Tools | |
| 505 | 8 | |a Chapter 35 An Introduction to Contemporary Mathematical LogicChapter 36 A Course in Model Theory; Chapter 37 Classes and Completeness; Chapter 38 Axioms; Chapter 39 The Incompleteness Theorems; Chapter 40 Conceptual Perspectives; Chapter 41 Programming Perspectives; Chapter 42 Advances in Linear Logic; Chapter 43 Symbolic Logic; Bibliography; Index | |
| 650 | 0 | |a Computer science |x Mathematics. |0 http://id.loc.gov/authorities/subjects/sh85042295 | |
| 650 | 6 | |a Informatique |x Mathématiques. | |
| 650 | 7 | |a Computer science |x Mathematics |2 fast | |
| 758 | |i has work: |a Computer Mathematics (Text) |1 https://id.oclc.org/worldcat/entity/E39PD3vfhgWXdBJYfQ6r8W8Fjy |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Prudhomme, Gerard. |t Computer Mathematics. |d Ashland : Arcler Press, ©2019 |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2013901 |3 Volltext |
| 938 | |a Askews and Holts Library Services |b ASKH |n BDZ0044473341 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5655507 | ||
| 938 | |a EBSCOhost |b EBSC |n 2013901 | ||
| 938 | |a YBP Library Services |b YANK |n 16023320 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-on1085219852 |
|---|---|
| _version_ | 1816882484525137922 |
| adam_text | |
| any_adam_object | |
| author | Prudhomme, Gerard |
| author_facet | Prudhomme, Gerard |
| author_role | |
| author_sort | Prudhomme, Gerard |
| author_variant | g p gp |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76.9.M35 |
| callnumber-search | QA76.9.M35 |
| callnumber-sort | QA 276.9 M35 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Cover; Half Title Page; Title Page; Copyright Page; About the Author; Table of Contents; List of Figures; Preface; Chapter 1 Preparatory Mathematical and Computer Science Studies; Chapter 2 Predictable Phenomena; 2.1. Intensive Preliminary Courses of Logic; Chapter 3 Theory of Models and of Groups; Chapter 4 Programming Models; Chapter 5 Introduction to Formal Computer-Aided Proof; Chapter 6 Theory of the Demonstration; 6.1. Calculability And Incompleteness; Chapter 7 Working Group on Core Courses; 7.1. Verifications; 7.2. Complexity; Chapter 8 Finite Model Theory Chapter 9 Calculability and IncompletenessChapter 10 Programming Models; Chapter 11 Combinators; Chapter 12 Mathematical Logic; Chapter 13 Foundations of Computing; Chapter 14 Formal Arithmetic; Chapter 15 Database Object Component; Chapter 16 Arithmetization of Logic; Chapter 17 Computability and Complexity; Chapter 18 Polarization and Classical Logic; Chapter 19 Syntax and Semantics; Chapter 20 Proofs and Types; Chapter 21 Foundations for Programming Languages; 21.1. Basic Set Theory; Chapter 22 Descriptive Set Theory; 22.1. Structures And Techniques Chapter 23 Semantics of Programming LanguagesChapter 24 Stable Groups; Chapter 25 General Theory of Algorithms; Chapter 26 Recursive Functions; 26.1. Machine-Calculable Functions; Chapter 27 Logical Characterization of Computable Functions; Chapter 28 Notions of Reduction and Undecidable Problems; Chapter 29 Introduction to Complexity; Chapter 30 Theory of Finite Models and Applications; Chapter 31 Approximate Verification and Complexity; Chapter 32 Working on Fundamental Courses; Chapter 33 Preliminary Intensive Logic; Chapter 34 Classic Tools Chapter 35 An Introduction to Contemporary Mathematical LogicChapter 36 A Course in Model Theory; Chapter 37 Classes and Completeness; Chapter 38 Axioms; Chapter 39 The Incompleteness Theorems; Chapter 40 Conceptual Perspectives; Chapter 41 Programming Perspectives; Chapter 42 Advances in Linear Logic; Chapter 43 Symbolic Logic; Bibliography; Index |
| ctrlnum | (OCoLC)1085219852 |
| dewey-full | 004.0151 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 004 - Computer science |
| dewey-raw | 004.0151 |
| dewey-search | 004.0151 |
| dewey-sort | 14.0151 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03857cam a2200469Mu 4500</leader><controlfield tag="001">ZDB-4-EBA-on1085219852</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr |n|---|||||</controlfield><controlfield tag="008">190209s2019 xx o 000 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">EBLCP</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">EBLCP</subfield><subfield code="d">YDX</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKAHL</subfield><subfield code="d">N$T</subfield><subfield code="d">OCLCO</subfield><subfield code="d">N$T</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCO</subfield><subfield code="d">K6U</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">1084502391</subfield><subfield code="a">1084694062</subfield><subfield code="a">1284938266</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1773615971</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781773615974</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1085219852</subfield><subfield code="z">(OCoLC)1084502391</subfield><subfield code="z">(OCoLC)1084694062</subfield><subfield code="z">(OCoLC)1284938266</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA76.9.M35</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">004.0151</subfield><subfield code="2">23</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Prudhomme, Gerard.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Computer Mathematics</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Ashland :</subfield><subfield code="b">Arcler Press,</subfield><subfield code="c">2019.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (268 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover; Half Title Page; Title Page; Copyright Page; About the Author; Table of Contents; List of Figures; Preface; Chapter 1 Preparatory Mathematical and Computer Science Studies; Chapter 2 Predictable Phenomena; 2.1. Intensive Preliminary Courses of Logic; Chapter 3 Theory of Models and of Groups; Chapter 4 Programming Models; Chapter 5 Introduction to Formal Computer-Aided Proof; Chapter 6 Theory of the Demonstration; 6.1. Calculability And Incompleteness; Chapter 7 Working Group on Core Courses; 7.1. Verifications; 7.2. Complexity; Chapter 8 Finite Model Theory</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Chapter 9 Calculability and IncompletenessChapter 10 Programming Models; Chapter 11 Combinators; Chapter 12 Mathematical Logic; Chapter 13 Foundations of Computing; Chapter 14 Formal Arithmetic; Chapter 15 Database Object Component; Chapter 16 Arithmetization of Logic; Chapter 17 Computability and Complexity; Chapter 18 Polarization and Classical Logic; Chapter 19 Syntax and Semantics; Chapter 20 Proofs and Types; Chapter 21 Foundations for Programming Languages; 21.1. Basic Set Theory; Chapter 22 Descriptive Set Theory; 22.1. Structures And Techniques</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Chapter 23 Semantics of Programming LanguagesChapter 24 Stable Groups; Chapter 25 General Theory of Algorithms; Chapter 26 Recursive Functions; 26.1. Machine-Calculable Functions; Chapter 27 Logical Characterization of Computable Functions; Chapter 28 Notions of Reduction and Undecidable Problems; Chapter 29 Introduction to Complexity; Chapter 30 Theory of Finite Models and Applications; Chapter 31 Approximate Verification and Complexity; Chapter 32 Working on Fundamental Courses; Chapter 33 Preliminary Intensive Logic; Chapter 34 Classic Tools</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Chapter 35 An Introduction to Contemporary Mathematical LogicChapter 36 A Course in Model Theory; Chapter 37 Classes and Completeness; Chapter 38 Axioms; Chapter 39 The Incompleteness Theorems; Chapter 40 Conceptual Perspectives; Chapter 41 Programming Perspectives; Chapter 42 Advances in Linear Logic; Chapter 43 Symbolic Logic; Bibliography; Index</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Computer science</subfield><subfield code="x">Mathematics.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85042295</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Informatique</subfield><subfield code="x">Mathématiques.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Computer science</subfield><subfield code="x">Mathematics</subfield><subfield code="2">fast</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Computer Mathematics (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PD3vfhgWXdBJYfQ6r8W8Fjy</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Prudhomme, Gerard.</subfield><subfield code="t">Computer Mathematics.</subfield><subfield code="d">Ashland : Arcler Press, ©2019</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2013901</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">BDZ0044473341</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest Ebook Central</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL5655507</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">2013901</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">16023320</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-on1085219852 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:29:21Z |
| institution | BVB |
| isbn | 1773615971 9781773615974 |
| language | English |
| oclc_num | 1085219852 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (268 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Arcler Press, |
| record_format | marc |
| spelling | Prudhomme, Gerard. Computer Mathematics Ashland : Arcler Press, 2019. 1 online resource (268 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Print version record. Cover; Half Title Page; Title Page; Copyright Page; About the Author; Table of Contents; List of Figures; Preface; Chapter 1 Preparatory Mathematical and Computer Science Studies; Chapter 2 Predictable Phenomena; 2.1. Intensive Preliminary Courses of Logic; Chapter 3 Theory of Models and of Groups; Chapter 4 Programming Models; Chapter 5 Introduction to Formal Computer-Aided Proof; Chapter 6 Theory of the Demonstration; 6.1. Calculability And Incompleteness; Chapter 7 Working Group on Core Courses; 7.1. Verifications; 7.2. Complexity; Chapter 8 Finite Model Theory Chapter 9 Calculability and IncompletenessChapter 10 Programming Models; Chapter 11 Combinators; Chapter 12 Mathematical Logic; Chapter 13 Foundations of Computing; Chapter 14 Formal Arithmetic; Chapter 15 Database Object Component; Chapter 16 Arithmetization of Logic; Chapter 17 Computability and Complexity; Chapter 18 Polarization and Classical Logic; Chapter 19 Syntax and Semantics; Chapter 20 Proofs and Types; Chapter 21 Foundations for Programming Languages; 21.1. Basic Set Theory; Chapter 22 Descriptive Set Theory; 22.1. Structures And Techniques Chapter 23 Semantics of Programming LanguagesChapter 24 Stable Groups; Chapter 25 General Theory of Algorithms; Chapter 26 Recursive Functions; 26.1. Machine-Calculable Functions; Chapter 27 Logical Characterization of Computable Functions; Chapter 28 Notions of Reduction and Undecidable Problems; Chapter 29 Introduction to Complexity; Chapter 30 Theory of Finite Models and Applications; Chapter 31 Approximate Verification and Complexity; Chapter 32 Working on Fundamental Courses; Chapter 33 Preliminary Intensive Logic; Chapter 34 Classic Tools Chapter 35 An Introduction to Contemporary Mathematical LogicChapter 36 A Course in Model Theory; Chapter 37 Classes and Completeness; Chapter 38 Axioms; Chapter 39 The Incompleteness Theorems; Chapter 40 Conceptual Perspectives; Chapter 41 Programming Perspectives; Chapter 42 Advances in Linear Logic; Chapter 43 Symbolic Logic; Bibliography; Index Computer science Mathematics. http://id.loc.gov/authorities/subjects/sh85042295 Informatique Mathématiques. Computer science Mathematics fast has work: Computer Mathematics (Text) https://id.oclc.org/worldcat/entity/E39PD3vfhgWXdBJYfQ6r8W8Fjy https://id.oclc.org/worldcat/ontology/hasWork Print version: Prudhomme, Gerard. Computer Mathematics. Ashland : Arcler Press, ©2019 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2013901 Volltext |
| spellingShingle | Prudhomme, Gerard Computer Mathematics Cover; Half Title Page; Title Page; Copyright Page; About the Author; Table of Contents; List of Figures; Preface; Chapter 1 Preparatory Mathematical and Computer Science Studies; Chapter 2 Predictable Phenomena; 2.1. Intensive Preliminary Courses of Logic; Chapter 3 Theory of Models and of Groups; Chapter 4 Programming Models; Chapter 5 Introduction to Formal Computer-Aided Proof; Chapter 6 Theory of the Demonstration; 6.1. Calculability And Incompleteness; Chapter 7 Working Group on Core Courses; 7.1. Verifications; 7.2. Complexity; Chapter 8 Finite Model Theory Chapter 9 Calculability and IncompletenessChapter 10 Programming Models; Chapter 11 Combinators; Chapter 12 Mathematical Logic; Chapter 13 Foundations of Computing; Chapter 14 Formal Arithmetic; Chapter 15 Database Object Component; Chapter 16 Arithmetization of Logic; Chapter 17 Computability and Complexity; Chapter 18 Polarization and Classical Logic; Chapter 19 Syntax and Semantics; Chapter 20 Proofs and Types; Chapter 21 Foundations for Programming Languages; 21.1. Basic Set Theory; Chapter 22 Descriptive Set Theory; 22.1. Structures And Techniques Chapter 23 Semantics of Programming LanguagesChapter 24 Stable Groups; Chapter 25 General Theory of Algorithms; Chapter 26 Recursive Functions; 26.1. Machine-Calculable Functions; Chapter 27 Logical Characterization of Computable Functions; Chapter 28 Notions of Reduction and Undecidable Problems; Chapter 29 Introduction to Complexity; Chapter 30 Theory of Finite Models and Applications; Chapter 31 Approximate Verification and Complexity; Chapter 32 Working on Fundamental Courses; Chapter 33 Preliminary Intensive Logic; Chapter 34 Classic Tools Chapter 35 An Introduction to Contemporary Mathematical LogicChapter 36 A Course in Model Theory; Chapter 37 Classes and Completeness; Chapter 38 Axioms; Chapter 39 The Incompleteness Theorems; Chapter 40 Conceptual Perspectives; Chapter 41 Programming Perspectives; Chapter 42 Advances in Linear Logic; Chapter 43 Symbolic Logic; Bibliography; Index Computer science Mathematics. http://id.loc.gov/authorities/subjects/sh85042295 Informatique Mathématiques. Computer science Mathematics fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85042295 |
| title | Computer Mathematics |
| title_auth | Computer Mathematics |
| title_exact_search | Computer Mathematics |
| title_full | Computer Mathematics |
| title_fullStr | Computer Mathematics |
| title_full_unstemmed | Computer Mathematics |
| title_short | Computer Mathematics |
| title_sort | computer mathematics |
| topic | Computer science Mathematics. http://id.loc.gov/authorities/subjects/sh85042295 Informatique Mathématiques. Computer science Mathematics fast |
| topic_facet | Computer science Mathematics. Informatique Mathématiques. Computer science Mathematics |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2013901 |
| work_keys_str_mv | AT prudhommegerard computermathematics |