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18.781 Theory of Numbers (MIT) 18.781 Theory of Numbers (MIT)

Description

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.    This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.   

Subjects

primes | primes | divisibility | divisibility | fundamental theorem of arithmetic | fundamental theorem of arithmetic | gcd | gcd | Euclidean algorithm | Euclidean algorithm | congruences | congruences | Chinese remainder theorem | Chinese remainder theorem | Hensel's lemma | Hensel's lemma | primitive roots | primitive roots | quadratic residues | quadratic residues | reciprocity | reciprocity | arithmetic functions | arithmetic functions | Diophantine equations | Diophantine equations | continued fractions | continued fractions

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates. This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.712 Introduction to Representation Theory (MIT) 18.712 Introduction to Representation Theory (MIT)

Description

The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces. The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.

Subjects

finite dimensional algebras | finite dimensional algebras | Quiver Representations | Quiver Representations | series Representations | series Representations | finite groups | finite groups | representation theory | representation theory | Lie algebras | Lie algebras | Tensor products | Tensor products | density theorem | density theorem | Jordan-H?older theorem | Jordan-H?older theorem | Krull-Schmidt theorem | Krull-Schmidt theorem | Maschke?s Theorem | Maschke?s Theorem | Frobenius-Schur indicator | Frobenius-Schur indicator | Frobenius divisibility | Frobenius divisibility | Burnside?s Theorem | Burnside?s Theorem

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates. This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.712 Introduction to Representation Theory (MIT) 18.712 Introduction to Representation Theory (MIT)

Description

This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces. This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.

Subjects

finite dimensional algebras | finite dimensional algebras | Quiver Representations | Quiver Representations | series Representations | series Representations | finite groups | finite groups | representation theory | representation theory | Lie algebras | Lie algebras | Tensor products | Tensor products | density theorem | density theorem | Jordan-H?older theorem | Jordan-H?older theorem | Krull-Schmidt theorem | Krull-Schmidt theorem | Maschke?s Theorem | Maschke?s Theorem | Frobenius-Schur indicator | Frobenius-Schur indicator | Frobenius divisibility | Frobenius divisibility | Burnside?s Theorem | Burnside?s Theorem

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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6.837 Computer Graphics (MIT) 6.837 Computer Graphics (MIT)

Description

6.837 offers an introduction to computer graphics hardware, algorithms, and software. Topics include: line generators, affine transformations, line and polygon clipping, splines, interactive techniques, perspective projection, solid modeling, hidden surface algorithms, lighting models, shading, and animation. Substantial programming experience is required. This course is worth 6 Engineering Design Points. 6.837 offers an introduction to computer graphics hardware, algorithms, and software. Topics include: line generators, affine transformations, line and polygon clipping, splines, interactive techniques, perspective projection, solid modeling, hidden surface algorithms, lighting models, shading, and animation. Substantial programming experience is required. This course is worth 6 Engineering Design Points.

Subjects

data structures; algorithms; presenting data visually; programming; computer graphics; computer graphics applications; ray tracing; ray casting; transformation; hierarchy | data structures; algorithms; presenting data visually; programming; computer graphics; computer graphics applications; ray tracing; ray casting; transformation; hierarchy | data structures | data structures | algorithms | algorithms | presenting data visually | presenting data visually | programming | programming | computer graphics | computer graphics | computer graphics applications | computer graphics applications | ray tracing | ray tracing | ray casting | ray casting | transformation | transformation | hierarchy | hierarchy | illumination | illumination | shading | shading | acceleration structures | acceleration structures | animation | animation | image-based rendering | image-based rendering | curves | curves | surfaces | surfaces | key frames | key frames | perspective | perspective | rasterization | rasterization | clipping | clipping | visibility | visibility | rendering | rendering | radiosity | radiosity | colors | colors | altialiasing | altialiasing | texture mapping | texture mapping | procedural textures | procedural textures | shadows | shadows | graphics hardware | graphics hardware

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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6.837 Computer Graphics (MIT)

Description

6.837 offers an introduction to computer graphics hardware, algorithms, and software. Topics include: line generators, affine transformations, line and polygon clipping, splines, interactive techniques, perspective projection, solid modeling, hidden surface algorithms, lighting models, shading, and animation. Substantial programming experience is required. This course is worth 6 Engineering Design Points.

Subjects

data structures; algorithms; presenting data visually; programming; computer graphics; computer graphics applications; ray tracing; ray casting; transformation; hierarchy | data structures | algorithms | presenting data visually | programming | computer graphics | computer graphics applications | ray tracing | ray casting | transformation | hierarchy | illumination | shading | acceleration structures | animation | image-based rendering | curves | surfaces | key frames | perspective | rasterization | clipping | visibility | rendering | radiosity | colors | altialiasing | texture mapping | procedural textures | shadows | graphics hardware

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Deljivost naravnih števil Divisibility of numbers

Description

Na tem delovnem listu najdete naloge, ki se nanašajo na večkranike in delitelje naravnih števil, praštevila ter razcep na prafaktorje. Different math exercises that require the knowledge of divisibility, prime and composite numbers, ...

Subjects

znanstvene vede | sciences | matematika | mathematics | deljenje | division | deljivost | divisibility | praštevilo | prime number | sestavljeno število | composite number

License

http://creativecommons.org/licenses/by-nc-sa/2.5/si/ http://creativecommons.org/licenses/by-nc-sa/2.5/si/

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Priprava na pisno ocenjevanje znanja - celoletna snov Math exercises

Description

Naloge za preverjanje znanja iz celoletne snovi v 7. razredu Collection of different exercises that require the wide knowledge of math (Percentage, shapes, fractions, ...).

Subjects

znanstvene vede | sciences | matematika | mathematics | odstotek | percentage | deljivost | divisibility | lik | shape | ulomek | fraction

License

http://creativecommons.org/licenses/by-nc-sa/2.5/si/ http://creativecommons.org/licenses/by-nc-sa/2.5/si/

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Napitek nevidnosti Elixir of invisibility

Description

Učenec lahko nalogo rešuje kar z računalnikom. Najprej shranite dokument na svoj računalnik, nato lahko ustvarja in popravlja po mili volji. Učni list pa lahko seveda tudi natisnete, vendar doadajte črte za ročno pisanje. Writing essay on events that can occur when drinking elixir of invisibility.

Subjects

jeziki | languages | moderni jeziki | modern languages | slovenski jezik | Slovene language | napitek | elixir | nevidnost | invisibility | domišljija | imagination | spis | essay

License

http://creativecommons.org/licenses/by-nc-sa/2.5/si/ http://creativecommons.org/licenses/by-nc-sa/2.5/si/

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6.837 Computer Graphics (MIT)

Description

6.837 offers an introduction to computer graphics hardware, algorithms, and software. Topics include: line generators, affine transformations, line and polygon clipping, splines, interactive techniques, perspective projection, solid modeling, hidden surface algorithms, lighting models, shading, and animation. Substantial programming experience is required. This course is worth 6 Engineering Design Points.

Subjects

data structures; algorithms; presenting data visually; programming; computer graphics; computer graphics applications; ray tracing; ray casting; transformation; hierarchy | data structures | algorithms | presenting data visually | programming | computer graphics | computer graphics applications | ray tracing | ray casting | transformation | hierarchy | illumination | shading | acceleration structures | animation | image-based rendering | curves | surfaces | key frames | perspective | rasterization | clipping | visibility | rendering | radiosity | colors | altialiasing | texture mapping | procedural textures | shadows | graphics hardware

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.781 Theory of Numbers (MIT)

Description

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.   

Subjects

primes | divisibility | fundamental theorem of arithmetic | gcd | Euclidean algorithm | congruences | Chinese remainder theorem | Hensel's lemma | primitive roots | quadratic residues | reciprocity | arithmetic functions | Diophantine equations | continued fractions

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.712 Introduction to Representation Theory (MIT)

Description

This is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.

Subjects

finite dimensional algebras | Quiver Representations | series Representations | finite groups | representation theory | Lie algebras | Tensor products | density theorem | Jordan-H?older theorem | Krull-Schmidt theorem | Maschke?s Theorem | Frobenius-Schur indicator | Frobenius divisibility | Burnside?s Theorem

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.712 Introduction to Representation Theory (MIT)

Description

The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.

Subjects

finite dimensional algebras | Quiver Representations | series Representations | finite groups | representation theory | Lie algebras | Tensor products | density theorem | Jordan-H?older theorem | Krull-Schmidt theorem | Maschke?s Theorem | Frobenius-Schur indicator | Frobenius divisibility | Burnside?s Theorem

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.S34 Problem Solving Seminar (MIT)

Description

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | probability | congruences and divisibility | recurrences | limits | greatest integer function | inequalities | Putnam practice | hidden independence | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.S34 Problem Solving Seminar (MIT)

Description

This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving.

Subjects

Pigeonhole Principle | probability | congruences and divisibility | recurrences | limits | greatest integer function | inequalities | Putnam practice | hidden independence | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Pravila za deljivost Divisibility rules

Description

PowerPointova diaprojekcija s predstavitvijo pravil za deljivost. Presentation of two basic divisibility rules (divisibility of multiplication and addition).

Subjects

znanstvene vede | sciences | matematika | mathematics | deljivost | divisibility | število | number | deljenje | division | pravilo | rule

License

http://creativecommons.org/licenses/by-nc-sa/2.5/si/ http://creativecommons.org/licenses/by-nc-sa/2.5/si/

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Praštevila in sestavljena števila Prime and composite numbers

Description

PowerPointova diaprojekcija s predstavitvijo in delitvijo števil na praštevila in sestavljena števila vsebuje tudi Eratostenovo rešeto. Presentation of prime and composite numbers, divisibility of prime numbers, searching prime numbers with sieve of Eratosthenes.

Subjects

znanstvene vede | sciences | matematika | mathematics | praštevilo | prime number | sestavljeno število | composite number | deljivost | divisibility | eratostenovo rešeto | sieve of eratosthenes

License

http://creativecommons.org/licenses/by-nc-sa/2.5/si/ http://creativecommons.org/licenses/by-nc-sa/2.5/si/

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18.S34 Problem Solving Seminar (MIT)

Description

This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | probability | congruences and divisibility | recurrences | limits | greatest integer function | inequalities | Putnam practice | hidden independence | roots of polynomials

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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online presence guidelines: A four step guide to taking control of your visibility

Description

Authors:  Sarah Goodier, Laura Czerniewicz These Guidelines take academics through a four step process to improving their online presence, and taking charge of their online visibility. Clicked 95 times. Last clicked 01/14/2015 - 19:47. Teaching & Learning Context:  This resource can be used as a teaching aid or part of workshop training for academics.

Subjects

Centre for Higher Education Development | Centre for Educational Technology | Downloadable Documents | Other | English | Post-secondary | online presence | online profile | online visibility

License

http://creativecommons.org/licenses/by-sa/2.5/za/

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6.837 Computer Graphics (MIT)

Description

6.837 offers an introduction to computer graphics hardware, algorithms, and software. Topics include: line generators, affine transformations, line and polygon clipping, splines, interactive techniques, perspective projection, solid modeling, hidden surface algorithms, lighting models, shading, and animation. Substantial programming experience is required. This course is worth 6 Engineering Design Points.

Subjects

data structures; algorithms; presenting data visually; programming; computer graphics; computer graphics applications; ray tracing; ray casting; transformation; hierarchy | data structures | algorithms | presenting data visually | programming | computer graphics | computer graphics applications | ray tracing | ray casting | transformation | hierarchy | illumination | shading | acceleration structures | animation | image-based rendering | curves | surfaces | key frames | perspective | rasterization | clipping | visibility | rendering | radiosity | colors | altialiasing | texture mapping | procedural textures | shadows | graphics hardware

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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6.837 Computer Graphics (MIT)

Description

6.837 offers an introduction to computer graphics hardware, algorithms, and software. Topics include: line generators, affine transformations, line and polygon clipping, splines, interactive techniques, perspective projection, solid modeling, hidden surface algorithms, lighting models, shading, and animation. Substantial programming experience is required. This course is worth 6 Engineering Design Points.

Subjects

data structures; algorithms; presenting data visually; programming; computer graphics; computer graphics applications; ray tracing; ray casting; transformation; hierarchy | data structures | algorithms | presenting data visually | programming | computer graphics | computer graphics applications | ray tracing | ray casting | transformation | hierarchy | illumination | shading | acceleration structures | animation | image-based rendering | curves | surfaces | key frames | perspective | rasterization | clipping | visibility | rendering | radiosity | colors | altialiasing | texture mapping | procedural textures | shadows | graphics hardware

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Discrete Structures

Description

This course describes discrete mathematics, which involves processes that consist of sequences of individual steps (as compared to calculus, which describes processes that change in a continuous manner). The principal topics presented in this course are logic and proof, induction and recursion, discrete probability, and finite state machines. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Computer Science 202)

Subjects

discrete structures | truth tables | negations | tautologies | conditional statements | modus ponens | modus tollens | generalization | specialization | elimination | quantified | quantifiers | number theory | divisibility | induction | sequences | notation | set theory | recursion | automata | Computer science | I100

License

Attribution 2.0 UK: England & Wales Attribution 2.0 UK: England & Wales http://creativecommons.org/licenses/by/2.0/uk/ http://creativecommons.org/licenses/by/2.0/uk/

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