Linear algebra learning recommendations - Revision history

Vipul: /* Parts of linear algebra and their relative importance */

2014-05-19T18:10:55Z

Parts of linear algebra and their relative importance

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	\| Regression \|\| Ordinary least squares regression and its matrix implementation. \|\| People learning linear algebra for the purpose of applying it in any context, such as the sciences (natural and social) or any context that involves experimentation, measurement, and statistics.		\| Regression \|\| Ordinary least squares regression and its matrix implementation. \|\| People learning linear algebra for the purpose of applying it in any context, such as the sciences (natural and social) or any context that involves experimentation, measurement, and statistics.
	\|-		\|-
	\| Advanced computational topics \|\| Determinants, eigenvalues, QR factorization, Gram-Schmidt process, Gram-Schmidt factorization, etc. \|\| Some application contexts, such as machine learning, and some sciences that rely on heavy statistical machinery.		\| Advanced computational topics \|\| Determinants, eigenvalues, QR factorization, Gram-Schmidt process, Gram-Schmidt factorization, singular value decomposition, etc. \|\| Some application contexts, such as machine learning, and some sciences that rely on heavy statistical machinery.
	\|-		\|-
	\| Theoretical linear algebra \|\| Same as the foundation topics, but done right from the beginning in the context of abstract spaces and with generic proofs rather than relying on the language of matrices. \|\| Useful if pursuing higher mathematics.		\| Theoretical linear algebra \|\| Same as the foundation topics, but done right from the beginning in the context of abstract spaces and with generic proofs rather than relying on the language of matrices. \|\| Useful if pursuing higher mathematics.

Vipul at 17:17, 9 January 2014

2014-01-09T17:17:05Z

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			{{subject learning recommendations\|linear algebra}}

	'''Linear algebra''' is an important mathematical topic with wide applicability to the natural and social sciences, and is the only topic outside of the calculus sequences that is widely studied by undergraduates who do not intend to major in mathematics. Although some computational background related to linear algebra is covered in school syllabi, the concepts of linear algebra at the college level can still be very difficult for students, because of the focus of most curricula on preparing students for calculus to the exclusion of other parts of mathematics. The course may be taken as follows:		'''Linear algebra''' is an important mathematical topic with wide applicability to the natural and social sciences, and is the only topic outside of the calculus sequences that is widely studied by undergraduates who do not intend to major in mathematics. Although some computational background related to linear algebra is covered in school syllabi, the concepts of linear algebra at the college level can still be very difficult for students, because of the focus of most curricula on preparing students for calculus to the exclusion of other parts of mathematics. The course may be taken as follows:

Vipul at 16:49, 9 January 2014

2014-01-09T16:49:02Z

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	* [[Online mathematics learning resources]]		* [[Online mathematics learning resources]]
	* [[Mathematics reading recommendations]]		* [[Mathematics reading recommendations]]
			* [[Learn mathematics well]]
	==Parts of linear algebra and their relative importance==		==Parts of linear algebra and their relative importance==

Vipul at 15:57, 9 January 2014

2014-01-09T15:57:40Z

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	* Undergraduates typically take linear algebra after completing single variable calculus and multivariable calculus, although calculus is not formally a prerequisite for linear algebra. In some places, linear algebra and multivariable calculus are taught together as a third semester calculus course. In some places, they are separate semester-length or quarter-length courses.		* Undergraduates typically take linear algebra after completing single variable calculus and multivariable calculus, although calculus is not formally a prerequisite for linear algebra. In some places, linear algebra and multivariable calculus are taught together as a third semester calculus course. In some places, they are separate semester-length or quarter-length courses.
	* Some undergraduates who intend to major in mathematics may not take a separate linear algebra course but may study parts of it in their analysis and abstract algebra courses.		* Some undergraduates who intend to major in mathematics may not take a separate linear algebra course but may study parts of it in their analysis and abstract algebra courses.
	* Some students who finish single variable calculus in 11th grade (junior year of high school) may study linear algebra in 12th grade (senior year of high school).		* Some students who finish single variable calculus in 11th grade (junior year of high school) may study linear algebra in 12th grade (senior year of high school). See our [[high school mathematics]] page for descriptions of common tracks taken by students doing mathematics in high school.
	* Other students might do a few linear algebra topics (solving systems of equations, matrices, determinants) as part of algebra courses in high school.		* Other students might do a few linear algebra topics (solving systems of equations, matrices, determinants) as part of algebra courses in high school.

Vipul at 15:56, 9 January 2014

2014-01-09T15:56:34Z

← Older revision		Revision as of 15:56, 9 January 2014
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	'''Linear algebra''' is an important mathematical topic with wide applicability to the natural and social sciences, and is the only topic outside of the calculus sequences that is widely studied by undergraduates who do not intend to major in mathematics. Although some computational background related to linear algebra is covered in school syllabi, the concepts of linear algebra at the college level can still be very difficult for students, because of the focus of most curricula on preparing students for calculus to the exclusion of other parts of mathematics. The course may be taken as follows:		'''Linear algebra''' is an important mathematical topic with wide applicability to the natural and social sciences, and is the only topic outside of the calculus sequences that is widely studied by undergraduates who do not intend to major in mathematics. Although some computational background related to linear algebra is covered in school syllabi, the concepts of linear algebra at the college level can still be very difficult for students, because of the focus of most curricula on preparing students for calculus to the exclusion of other parts of mathematics. The course may be taken as follows:

	* Undergraduates typically take linear algebra after completing single variable calculus and multivariable calculus, although calculus is not formally a prerequisite for linear algebra.		* Undergraduates typically take linear algebra after completing single variable calculus and multivariable calculus, although calculus is not formally a prerequisite for linear algebra. In some places, linear algebra and multivariable calculus are taught together as a third semester calculus course. In some places, they are separate semester-length or quarter-length courses.
			* Some undergraduates who intend to major in mathematics may not take a separate linear algebra course but may study parts of it in their analysis and abstract algebra courses.
	* Some students who finish single variable calculus in 11th grade (junior year of high school) may study linear algebra in 12th grade (senior year of high school).		* Some students who finish single variable calculus in 11th grade (junior year of high school) may study linear algebra in 12th grade (senior year of high school).
	* Other students might do a few linear algebra topics (solving systems of equations, matrices, determinants) as part of algebra courses in high school.		* Other students might do a few linear algebra topics (solving systems of equations, matrices, determinants) as part of algebra courses in high school.

Vipul at 15:46, 9 January 2014

2014-01-09T15:46:07Z

← Older revision		Revision as of 15:46, 9 January 2014
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	This page includes some guidance on who needs to learn linear algebra, what parts of linear algebra are important,resource suggestions for people interested in learning linear algebra.		This page includes some guidance on who needs to learn linear algebra, what parts of linear algebra are important,resource suggestions for people interested in learning linear algebra.

			See also:

			* [[Calculus learning recommendations]]
			* [[Multivariable calculus learning recommendations]]
			* [[Online mathematics learning resources]]
			* [[Mathematics reading recommendations]]
	==Parts of linear algebra and their relative importance==		==Parts of linear algebra and their relative importance==

Vipul at 15:45, 9 January 2014

2014-01-09T15:45:27Z

← Older revision		Revision as of 15:45, 9 January 2014
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	'''Linear algebra''' is an important mathematical topic with wide applicability to the natural and social sciences, and is the only topic outside of the calculus sequences that is widely studied by undergraduates who do not intend to major in mathematics. Although some computational background related to linear algebra is covered in school syllabi, the concepts of linear algebra at the college level can still be very difficult for students, because of the focus of most curricula on preparing students for calculus to the exclusion of other parts of mathematics.		'''Linear algebra''' is an important mathematical topic with wide applicability to the natural and social sciences, and is the only topic outside of the calculus sequences that is widely studied by undergraduates who do not intend to major in mathematics. Although some computational background related to linear algebra is covered in school syllabi, the concepts of linear algebra at the college level can still be very difficult for students, because of the focus of most curricula on preparing students for calculus to the exclusion of other parts of mathematics. The course may be taken as follows:

			* Undergraduates typically take linear algebra after completing single variable calculus and multivariable calculus, although calculus is not formally a prerequisite for linear algebra.
			* Some students who finish single variable calculus in 11th grade (junior year of high school) may study linear algebra in 12th grade (senior year of high school).
			* Other students might do a few linear algebra topics (solving systems of equations, matrices, determinants) as part of algebra courses in high school.

	This page includes some guidance on who needs to learn linear algebra, what parts of linear algebra are important,resource suggestions for people interested in learning linear algebra.		This page includes some guidance on who needs to learn linear algebra, what parts of linear algebra are important,resource suggestions for people interested in learning linear algebra.

Vipul: /* Recommendations for learning linear algebra with an application orientation (includes general purpose recommendations) */

2014-01-09T07:03:01Z

Recommendations for learning linear algebra with an application orientation (includes general purpose recommendations)

← Older revision		Revision as of 07:03, 9 January 2014
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	* The foundation topics and regression are covered in [http://vipulnaik.com/math-196 Vipul Naik's online Math 196 notes]. These provide considerable insight into linear algebra from a statistical application-oriented view, without including any statistics. However, due to the paucity of worked examples, these are best studied in conjunction with a book that has worked examples.		* The foundation topics and regression are covered in [http://vipulnaik.com/math-196 Vipul Naik's online Math 196 notes]. These provide considerable insight into linear algebra from a statistical application-oriented view, without including any statistics. However, due to the paucity of worked examples, these are best studied in conjunction with a book that has worked examples.
	* [http://centerofmath.org/textbooks/ela/index.html Center of Math linear algebra text]		* [http://centerofmath.org/textbooks/ela/index.html Center of Math linear algebra text]
	* [http://www.amazon.com/Algebra-Applications-Edition-Featured-Introductory/dp/0321796977~~/ref=dp_ob_title_bk Linear Algebra with Applications (5th Edition~~)] by Otto Bretscher is a reasonably decent book (it is also synced with Vipul Naik's online notes, though it may not be worth buying just for that purpose).		* ''Linear Algebra with Applications (5th Edition)'' ([http://www.amazon.com/Algebra-Applications-Edition-Featured-Introductory/dp/0321796977 Amazon]) by Otto Bretscher is a reasonably decent book (it is also synced with Vipul Naik's online notes, though it may not be worth buying just for that purpose).

Vipul: /* =Recommendations for learning theoretically oriented linear algebra */

2014-01-09T07:02:26Z

=Recommendations for learning theoretically oriented linear algebra

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	==Recommendations==		==Recommendations==

	===Recommendations for learning theoretically oriented linear algebra==		===Recommendations for learning theoretically oriented linear algebra===

	* ''Linear Algebra Done Right'' by Sheldon Axler ([http://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mathematics/dp/0387982582 Amazon])		* ''Linear Algebra Done Right'' by Sheldon Axler ([http://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mathematics/dp/0387982582 Amazon])

Vipul at 07:02, 9 January 2014

2014-01-09T07:02:02Z

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 | Advanced computational topics || Determinants, eigenvalues, QR factorization, Gram-Schmidt process, Gram-Schmidt factorization, etc. || Some application contexts, such as machine learning, and some sciences that rely on heavy statistical machinery.
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