Undergraduate mathematics - Revision history

Vipul at 19:09, 13 February 2014

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-This page provides an overview of the typical course structure that people pursuing undergraduate studies in mathematics have, along with important points of difference between different colleges in how they structure their programs.
+Undergraduate mathematics has two main parts:
-==Beginning non-major-specific material==
+* [[Lower division undergraduate mathematics]] includes calculus, multivariable calculus, linear algebra, and ordinary differential equations. The courses at this level are taken by many people who do not intend to major in mathematics.
+* [[Upper division undergraduate mathematics]] includes abstract algebra, undergraduate analysis, topology, and more high-level mathematics.

Vipul: /* Beginning non-major-specific material */

2014-01-11T02:59:19Z

Beginning non-major-specific material

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	* Multivariable calculus		* Multivariable calculus
	* Linear algebra		* Linear algebra
	* ~~Differential~~ equations (for some majors)		* Ordinary differential equations (for some majors)

	These topics are also studied by many students who do not intend to major in mathematics. The following are some variations:		These topics are also studied by many students who do not intend to major in mathematics. The following are some variations:

Vipul: /* Major-specific material */

2014-01-11T02:58:15Z

Major-specific material

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	#* Analysis: Complex analysis, functional analysis, partial differential equations, analytic number theory		#* Analysis: Complex analysis, functional analysis, partial differential equations, analytic number theory
	#* Algebra: Commutative algebra, algebraic geometry, algebraic number theory		#* Algebra: Commutative algebra, algebraic geometry, algebraic number theory
	#* ~~Close to computer science: Logic~~, ~~discrete~~ mathematics and combinatorics		#* Set theory, logic
	#* ~~Close~~ to statistics~~: probability theory~~		#* Discrete mathematics and combinatorics (close to computer science)
			#* Probability theory (close to statistics)
	#* Other applied: Numerical analysis, Linear programming and optimization		#* Other applied: Numerical analysis, Linear programming and optimization
	# Mathematics students may be required or encouraged to take courses in sister subjects such as statistics and computer science.		# Mathematics students may be required or encouraged to take courses in sister subjects such as statistics and computer science.

	In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.		In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.

Vipul: /* Major-specific material */

2014-01-11T02:57:03Z

Major-specific material

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	# A number of other topics such as those listed below. The range of courses offered, and the degree of flexibility students have, depend on the college.		# A number of other topics such as those listed below. The range of courses offered, and the degree of flexibility students have, depend on the college.
	#* Topology/geometry: Topology (point set topology + a glimpse of algebraic topology), differential geometry		#* Topology/geometry: Topology (point set topology + a glimpse of algebraic topology), differential geometry
	#* Analysis: Complex analysis, functional analysis, analytic number theory		#* Analysis: Complex analysis, functional analysis, partial differential equations, analytic number theory
	#* Algebra: Commutative algebra, algebraic geometry, algebraic number ~~theor~~		#* Algebra: Commutative algebra, algebraic geometry, algebraic number theory
	#* Close to computer science: Logic, discrete mathematics and combinatorics		#* Close to computer science: Logic, discrete mathematics and combinatorics
	#* Close to statistics: probability theory		#* Close to statistics: probability theory
	#* Other applied: Numerical analysis		#* Other applied: Numerical analysis, Linear programming and optimization
	# Mathematics students may be required or encouraged to take courses in sister subjects such as statistics and computer science.		# Mathematics students may be required or encouraged to take courses in sister subjects such as statistics and computer science.

	In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.		In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.

Vipul: /* Major-specific material */

2014-01-11T02:56:08Z

Major-specific material

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	#* Topology/geometry: Topology (point set topology + a glimpse of algebraic topology), differential geometry		#* Topology/geometry: Topology (point set topology + a glimpse of algebraic topology), differential geometry
	#* Analysis: Complex analysis, functional analysis, analytic number theory		#* Analysis: Complex analysis, functional analysis, analytic number theory
	#* Algebra: Commutative algebra, algebraic geometry, algebraic number ~~theory~~		#* Algebra: Commutative algebra, algebraic geometry, algebraic number theor
	#* ~~Applied side~~: ~~Discrete~~ mathematics and combinatorics, probability theory~~, numerical~~ analysis		#* Close to computer science: Logic, discrete mathematics and combinatorics
			#* Close to statistics: probability theory
			#* Other applied: Numerical analysis
	# Mathematics students may be required or encouraged to take courses in sister subjects such as statistics and computer science.		# Mathematics students may be required or encouraged to take courses in sister subjects such as statistics and computer science.

	In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.		In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.

Vipul: /* Major-specific material */

2014-01-11T02:55:18Z

Major-specific material

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	# A year of real analysis: This includes some topological, measure-theoretic, and metric concepts associated with the real line, and an understanding of the real numbers and spaces like <math>\R^n</math> in that context. Some multivariable calculus and linear algebra may be covered here.		# A year of real analysis: This includes some topological, measure-theoretic, and metric concepts associated with the real line, and an understanding of the real numbers and spaces like <math>\R^n</math> in that context. Some multivariable calculus and linear algebra may be covered here.
	# A year of abstract algebra: This includes group theory, ring theory, and field theory. Some linear algebra may be covered here.		# A year of abstract algebra: This includes group theory, ring theory, and field theory. Some linear algebra may be covered here.
	# A number of other topics such as ~~topology~~ (point set topology + a glimpse of algebraic topology), ~~complex~~ analysis, functional analysis, ~~commutative~~ algebra, ~~differential~~ geometry, ~~discrete~~ mathematics and combinatorics, probability theory, ~~algebraic number theory, analytic number theory, etc. The range of courses offered, and the degree of flexibility students have, depend on the college.~~		# A number of other topics such as those listed below. The range of courses offered, and the degree of flexibility students have, depend on the college.
			#* Topology/geometry: Topology (point set topology + a glimpse of algebraic topology), differential geometry
			#* Analysis: Complex analysis, functional analysis, analytic number theory
			#* Algebra: Commutative algebra, algebraic geometry, algebraic number theory
			#* Applied side: Discrete mathematics and combinatorics, probability theory, numerical analysis
	# Mathematics students may be required or encouraged to take courses in sister subjects such as statistics and computer science.		# Mathematics students may be required or encouraged to take courses in sister subjects such as statistics and computer science.

	In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.		In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.

Vipul: /* Major-specific material */

2014-01-11T02:53:00Z

Major-specific material

← Older revision		Revision as of 02:53, 11 January 2014
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	# A year of real analysis: This includes some topological, measure-theoretic, and metric concepts associated with the real line, and an understanding of the real numbers and spaces like <math>\R^n</math> in that context. Some multivariable calculus and linear algebra may be covered here.		# A year of real analysis: This includes some topological, measure-theoretic, and metric concepts associated with the real line, and an understanding of the real numbers and spaces like <math>\R^n</math> in that context. Some multivariable calculus and linear algebra may be covered here.
	# A year of abstract algebra: This includes group theory, ring theory, and field theory. Some linear algebra may be covered here.		# A year of abstract algebra: This includes group theory, ring theory, and field theory. Some linear algebra may be covered here.
	# A number of other topics such as topology (point set topology + a glimpse of algebraic topology), complex analysis, functional analysis, commutative algebra, differential geometry, discrete mathematics and combinatorics, algebraic number theory, analytic number theory, etc. The range of courses offered, and the degree of flexibility students have, depend on the college.		# A number of other topics such as topology (point set topology + a glimpse of algebraic topology), complex analysis, functional analysis, commutative algebra, differential geometry, discrete mathematics and combinatorics, probability theory, algebraic number theory, analytic number theory, etc. The range of courses offered, and the degree of flexibility students have, depend on the college.
			# Mathematics students may be required or encouraged to take courses in sister subjects such as statistics and computer science.

	In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.		In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.

Vipul: /* Major-specific material */

2014-01-11T02:51:13Z

Major-specific material

← Older revision		Revision as of 02:51, 11 January 2014
Line 23:		Line 23:
	# A year of real analysis: This includes some topological, measure-theoretic, and metric concepts associated with the real line, and an understanding of the real numbers and spaces like <math>\R^n</math> in that context. Some multivariable calculus and linear algebra may be covered here.		# A year of real analysis: This includes some topological, measure-theoretic, and metric concepts associated with the real line, and an understanding of the real numbers and spaces like <math>\R^n</math> in that context. Some multivariable calculus and linear algebra may be covered here.
	# A year of abstract algebra: This includes group theory, ring theory, and field theory. Some linear algebra may be covered here.		# A year of abstract algebra: This includes group theory, ring theory, and field theory. Some linear algebra may be covered here.
	# A number of other topics such as topology (point set topology + a glimpse of algebraic topology), complex analysis, functional analysis, commutative algebra, differential geometry, algebraic number theory, analytic number theory, etc. The range of courses offered, and the degree of flexibility students have, depend on the college.		# A number of other topics such as topology (point set topology + a glimpse of algebraic topology), complex analysis, functional analysis, commutative algebra, differential geometry, discrete mathematics and combinatorics, algebraic number theory, analytic number theory, etc. The range of courses offered, and the degree of flexibility students have, depend on the college.

	In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.		In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.

Vipul: Created page with "This page provides an overview of the typical course structure that people pursuing undergraduate studies in mathematics have, along with important points of difference betwee..."

2014-01-11T01:56:00Z

Created page with "This page provides an overview of the typical course structure that people pursuing undergraduate studies in mathematics have, along with important points of difference betwee..."

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This page provides an overview of the typical course structure that people pursuing undergraduate studies in mathematics have, along with important points of difference between different colleges in how they structure their programs.

==Beginning non-major-specific material==

This includes:

* Single-variable calculus
* Multivariable calculus
* Linear algebra
* Differential equations (for some majors)

These topics are also studied by many students who do not intend to major in mathematics. The following are some variations:

# Some colleges allow students to place out of single-variable and multivariable calculus courses based on credit from exams taken in high school (such as the Advanced Placement or International Baccalaureate) or from placement examinations conducted by the college. Generally, students who intend to major in mathematics are more likely to avail of the opportunity to place out so that they can start their major-specific studies more quickly (they are also more likely to be qualified to place out).
# Some colleges have slightly different versions of these courses targeted at students who intend to major in mathematics:
#* There may be an "honors" version of single-variable calculus (and in some cases also of multivariable calculus and linear algebra) that is more heavily focused on proofs.
#* In some colleges, the multivariable calculus and linear algebra classes are not targeted at mathematics majors. Instead, mathematics majors are exposed to these topics as part of their analysis sequence. This means that the students can get started more quickly on their major-specific courses.

==Major-specific material==

Major-specific material typically includes:

# A year of real analysis: This includes some topological, measure-theoretic, and metric concepts associated with the real line, and an understanding of the real numbers and spaces like <math>\R^n</math> in that context. Some multivariable calculus and linear algebra may be covered here.
# A year of abstract algebra: This includes group theory, ring theory, and field theory. Some linear algebra may be covered here.
# A number of other topics such as topology (point set topology + a glimpse of algebraic topology), complex analysis, functional analysis, commutative algebra, differential geometry, algebraic number theory, analytic number theory, etc. The range of courses offered, and the degree of flexibility students have, depend on the college.

In some colleges, the convention is to do the year of real analysis first, and then proceed to the year of abstract algebra. In other colleges, the year of abstract algebra precedes the year of real analysis. In yet other places, the courses may be mixed with each other. Generally, whichever sequence is taught first will also have the responsibility of giving students some general mathematical knowledge (set theory, logic, proof-writing). Places that have an honors calculus option may use that to provide general mathematical knowledge.