Lower division undergraduate mathematics course structure - Revision history

Vipul: /* Pre-college recommendations */

2014-05-19T20:46:14Z

Pre-college recommendations

← Older revision		Revision as of 20:46, 19 May 2014
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	* Make sure to take, and prepare well for, the '''Advanced Placement BC Calculus examination''' in high school, if available to you: The placement options this opens up constitute an added reason to take the test. Take a look at our [[single-variable calculus learning recommendations]] for suggestions on how to prepare well.		* Make sure to take, and prepare well for, the '''Advanced Placement BC Calculus examination''' in high school, if available to you: The placement options this opens up constitute an added reason to take the test. Take a look at our [[single-variable calculus learning recommendations]] for suggestions on how to prepare well.
	* Make sure to '''review calculus quickly in the month or two prior to joining college''': This is particularly important for people who take AP Calculus in their junior year, or take a gap year after school. But even for people who took AP Calculus (or equivalent) in their senior year a few months ago, a lot can be forgotten over a few months. A quick refresher can be helpful both for doing well on on-campus placement tests and for getting off to a good start in college mathematics.		* Make sure to '''review calculus quickly in the month or two prior to joining college''': This is particularly important for people who take AP Calculus in their junior year, or [[taking a gap year between high school and college\|take a gap year after school]]. But even for people who took AP Calculus (or equivalent) in their senior year a few months ago, a lot can be forgotten over a few months. A quick refresher can be helpful both for doing well on on-campus placement tests and for getting off to a good start in college mathematics.
	* In the run-up to beginning college, '''give more emphasis to reviewing precalculus and single-variable calculus than to reviewing multivariable calculus and linear algebra''': Colleges generally grant credit and placement for single-variable calculus, but are less likely to grant credit or give placement based on multivariable calculus and linear algebra (there are some exceptions, such as MIT). Moreover, precalculus and single-variable calculus have wider applicability, so making sure you are thorough on these prepares you for a wider range of starting points.		* In the run-up to beginning college, '''give more emphasis to reviewing precalculus and single-variable calculus than to reviewing multivariable calculus and linear algebra''': Colleges generally grant credit and placement for single-variable calculus, but are less likely to grant credit or give placement based on multivariable calculus and linear algebra (there are some exceptions, such as MIT). Moreover, precalculus and single-variable calculus have wider applicability, so making sure you are thorough on these prepares you for a wider range of starting points.

Vipul: /* Placement and credit */

2014-05-19T20:44:44Z

Placement and credit

← Older revision		Revision as of 20:44, 19 May 2014
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	===Placement and credit===		===Placement and credit===

			<tt>See also [[college course dependencies]]</tt>

	Due to significant differences in the level of mathematical skill and preparation of entering undergraduates, colleges typically rely on some mechanisms to place students in the most suitable starting course. The mechanism include a combination of:		Due to significant differences in the level of mathematical skill and preparation of entering undergraduates, colleges typically rely on some mechanisms to place students in the most suitable starting course. The mechanism include a combination of:

Vipul: /* Some example university course structures */

2014-04-28T15:30:08Z

Some example university course structures

← Older revision		Revision as of 15:30, 28 April 2014
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! University !! Quarter or semester system? !! Regular single-variable sequence !! Regular sequence for multivariable calculus and linear algebra !!Honors route		! University !! [[Quarter versus semester system\|Quarter or semester system]]? !! Regular single-variable sequence !! Regular sequence for multivariable calculus and linear algebra !!Honors route
	\|-		\|-
	\| [http://www.math.princeton.edu/undergraduate/overview-lower-division-courses Princeton University] \|\|Semester \|\| 103-104 (optionally take 102 instead of the sequence) \|\| 201-202 (multivariable calculus and linear algebra for scientists) or 175 (multivariable calculus and linear algebra for social scientists) \|\| No honors substitute for 103-104 (but it can be placed out of)<br>203-204 is an "honors" replacement of 201-202, targeting at physicists and applied math people; 214-215 is the recommended option for people interested in theoretical mathematics (See [http://www.math.princeton.edu/undergraduate/placement/using-bc-calculus-scores here])		\| [http://www.math.princeton.edu/undergraduate/overview-lower-division-courses Princeton University] \|\|Semester \|\| 103-104 (optionally take 102 instead of the sequence) \|\| 201-202 (multivariable calculus and linear algebra for scientists) or 175 (multivariable calculus and linear algebra for social scientists) \|\| No honors substitute for 103-104 (but it can be placed out of)<br>203-204 is an "honors" replacement of 201-202, targeting at physicists and applied math people; 214-215 is the recommended option for people interested in theoretical mathematics (See [http://www.math.princeton.edu/undergraduate/placement/using-bc-calculus-scores here])

Vipul: /* Entry point decisions */

2014-04-25T17:30:13Z

Entry point decisions

← Older revision		Revision as of 17:30, 25 April 2014
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	* '''Understand the amount of flexibility''' that colleges offer with respect to placement. For instance, Stanford is highly flexible about placement levels -- many courses have open enrollment, and almost all courses allow you to enroll with instructor consent. The University of Chicago has prerequisites that are rigid on paper (people are required to have placement credit to begin specific courses) but students can request to try out a course one level higher, and can officially have their placement changed if they do well in the first few weeks of the course. Some aspects of this flexibility may not be evident from online materials, so talking to people can help.		* '''Understand the amount of flexibility''' that colleges offer with respect to placement. For instance, Stanford is highly flexible about placement levels -- many courses have open enrollment, and almost all courses allow you to enroll with instructor consent. The University of Chicago has prerequisites that are rigid on paper (people are required to have placement credit to begin specific courses) but students can request to try out a course one level higher, and can officially have their placement changed if they do well in the first few weeks of the course. Some aspects of this flexibility may not be evident from online materials, so talking to people can help.
	* To the extent that there is flexibility, use it to figure out your best option, rather than simply accepting the college recommendation (but give strong weight to the college recommendation as an informed piece of advice). ''However'', if you are doing this, you need to put in some prior effort in understanding the options. You should also have more willingness to change course if something unusual you tried out isn't working.		* To the extent that there is flexibility, use it to figure out your best option, rather than simply accepting the college recommendation (but give strong weight to the college recommendation as an informed piece of advice). ''However'', if you are doing this, you need to put in some prior effort in understanding the options. You should also have more willingness to change course if something unusual you tried out isn't working.
	* '''Understand the extent to which ordinary (non-honors) courses cover material well''': At top universities, the regular (non-honors) sequences can be fairly challenging in and of themselves, and it is not necessary to take the honors sequence to challenge oneself mathematically. In addition, ~~they~~ cover most mathematical topics relevant outside of mathematics, and students can generally enjoy the benefits of reasonably good peer groups. At mid-tier universities, the honors class might be the only place that provides adequate mathematical challenge and an interested and motivated peer group. Note that you should still consider honors options if you are interested in a math-based discipline or if it is the recommended placement you receive.		* '''Understand the extent to which ordinary (non-honors) courses cover material well''': At top universities, the regular (non-honors) sequences can be fairly challenging in and of themselves, and it is not necessary to take the honors sequence to challenge oneself mathematically. In addition, non-honors courses cover most mathematical topics relevant outside of mathematics, and students can generally enjoy the benefits of reasonably good peer groups. At mid-tier universities, the honors class might be the only place that provides adequate mathematical challenge and an interested and motivated peer group. Note that, regardless of your university, you should still consider honors options if you are interested in a math-based discipline or if it is the recommended placement you receive.

	===Once you get started===		===Once you get started===

Vipul at 17:23, 25 April 2014

2014-04-25T17:23:18Z

← Older revision		Revision as of 17:23, 25 April 2014
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	This page gives information on the course structure for [[lower division undergraduate mathematics]] courses, including calculus~~, multivariable~~ calculus~~, linear~~ algebra~~, and ordinary~~ differential equations.		This page gives information on the course structure for [[lower division undergraduate mathematics]] courses, including:

			* [[Single-variable calculus]]
			* [[Multivariable calculus]]
			* [[Linear algebra]]
			* [[Ordinary differential equations]]

	The information on this page has been constructed based on an in-depth knowledge of the course structure of a few undergraduate programs and a broad survey of many others. The program surveyed have been based in the United States. The structure of undergraduate programs differs from country to country and even varies widely within country, so please do ''not'' treat this as a substitute for information about the course structure at a specific educational institution.		The information on this page has been constructed based on an in-depth knowledge of the course structure of a few undergraduate programs and a broad survey of many others. The program surveyed have been based in the United States. The structure of undergraduate programs differs from country to country and even varies widely within country, so please do ''not'' treat this as a substitute for information about the course structure at a specific educational institution.

Vipul: /* Pre-college recommendations */

2014-04-25T17:22:39Z

Pre-college recommendations

← Older revision		Revision as of 17:22, 25 April 2014
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	Your choices earlier on can affect the options you have to get started:		Your choices earlier on can affect the options you have to get started:

	* Make sure to take, and prepare well for, the '''Advanced Placement BC Calculus examination''' in high school, if available to you: The placement options this opens up constitute an added reason to take the test. Take a look at our [[calculus learning recommendations]] for suggestions on how to prepare well.		* Make sure to take, and prepare well for, the '''Advanced Placement BC Calculus examination''' in high school, if available to you: The placement options this opens up constitute an added reason to take the test. Take a look at our [[single-variable calculus learning recommendations]] for suggestions on how to prepare well.
	* Make sure to '''review calculus quickly in the month or two prior to joining college''': This is particularly important for people who take AP Calculus in their junior year, or take a gap year after school. But even for people who took AP Calculus (or equivalent) in their senior year a few months ago, a lot can be forgotten over a few months. A quick refresher can be helpful both for doing well on on-campus placement tests and for getting off to a good start in college mathematics.		* Make sure to '''review calculus quickly in the month or two prior to joining college''': This is particularly important for people who take AP Calculus in their junior year, or take a gap year after school. But even for people who took AP Calculus (or equivalent) in their senior year a few months ago, a lot can be forgotten over a few months. A quick refresher can be helpful both for doing well on on-campus placement tests and for getting off to a good start in college mathematics.
	* In the run-up to beginning college, '''give more emphasis to reviewing precalculus and single-variable calculus than to reviewing multivariable calculus and linear algebra''': Colleges generally grant credit and placement for single-variable calculus, but are less likely to grant credit or give placement based on multivariable calculus and linear algebra (there are some exceptions, such as MIT). Moreover, precalculus and single-variable calculus have wider applicability, so making sure you are thorough on these prepares you for a wider range of starting points.		* In the run-up to beginning college, '''give more emphasis to reviewing precalculus and single-variable calculus than to reviewing multivariable calculus and linear algebra''': Colleges generally grant credit and placement for single-variable calculus, but are less likely to grant credit or give placement based on multivariable calculus and linear algebra (there are some exceptions, such as MIT). Moreover, precalculus and single-variable calculus have wider applicability, so making sure you are thorough on these prepares you for a wider range of starting points.

Vipul: /* Some example university course structures */

2014-02-14T01:41:57Z

Some example university course structures

← Older revision		Revision as of 01:41, 14 February 2014
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	\| [http://math.mit.edu/academics/classes.php Massachusetts Institute of Technology (MIT)] \|\| Semester \|\| 18.01 \|\| 18.02 (multivariable calculus), 18.03 (differential equations), 18.04 (linear algebra) \|\| 18.024, the "Calculus with Theory" course		\| [http://math.mit.edu/academics/classes.php Massachusetts Institute of Technology (MIT)] \|\| Semester \|\| 18.01 \|\| 18.02 (multivariable calculus), 18.03 (differential equations), 18.04 (linear algebra) \|\| 18.024, the "Calculus with Theory" course
	\|-		\|-
	\| [http://math.berkeley.edu/programs/undergraduate/minoring-mathematics ~~University of California~~, ~~Berkeley~~] \|\| Semester \|\| 1A and 1B \|\| 53 and 54 \|\| ?		\| University of California, Berkeley ([http://math.berkeley.edu/programs/undergraduate/minoring-mathematics here], [http://math.berkeley.edu/courses/choosing/honors-courses here]) \|\| Semester \|\| 1A and 1B \|\| 53 and 54 \|\| Honors versions of the courses 1B onward. However, these are offered sporadically, and there is no predefined guideline on how these differ from the regular sequence.
	\|-		\|-
	\| University of Michigan ([http://www.lsa.umich.edu/math/undergrad/coursesforfreshmen here], [http://www.lsa.umich.edu/math/undergrad/coursesforfreshmen/infinstandardcalcsequence here], and [http://www.lsa.umich.edu/math/undergrad/coursesforfreshmen here]) \|\| Semester \|\| 115 and 116 \|\| 215, 217, 316 \|\| 185, 186 (there are also other options)		\| University of Michigan ([http://www.lsa.umich.edu/math/undergrad/coursesforfreshmen here], [http://www.lsa.umich.edu/math/undergrad/coursesforfreshmen/infinstandardcalcsequence here], and [http://www.lsa.umich.edu/math/undergrad/coursesforfreshmen here]) \|\| Semester \|\| 115 and 116 \|\| 215, 217, 316 \|\| 185, 186 (there are also other options)
	\|}		\|}

Vipul: /* Some example university course structures */

2014-02-14T01:12:35Z

Some example university course structures

← Older revision		Revision as of 01:12, 14 February 2014
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	\|-		\|-
	\| [http://math.berkeley.edu/programs/undergraduate/minoring-mathematics University of California, Berkeley] \|\| Semester \|\| 1A and 1B \|\| 53 and 54 \|\| ?		\| [http://math.berkeley.edu/programs/undergraduate/minoring-mathematics University of California, Berkeley] \|\| Semester \|\| 1A and 1B \|\| 53 and 54 \|\| ?
			\|-
			\| University of Michigan ([http://www.lsa.umich.edu/math/undergrad/coursesforfreshmen here], [http://www.lsa.umich.edu/math/undergrad/coursesforfreshmen/infinstandardcalcsequence here], and [http://www.lsa.umich.edu/math/undergrad/coursesforfreshmen here]) \|\| Semester \|\| 115 and 116 \|\| 215, 217, 316 \|\| 185, 186 (there are also other options)
	\|}		\|}

Vipul at 00:05, 14 February 2014

2014-02-14T00:05:18Z

← Older revision		Revision as of 00:05, 14 February 2014
Line 1:		Line 1:
			This page gives information on the course structure for [[lower division undergraduate mathematics]] courses, including calculus, multivariable calculus, linear algebra, and ordinary differential equations.

	The information on this page has been constructed based on an in-depth knowledge of the course structure of a few undergraduate programs and a broad survey of many others. The program surveyed have been based in the United States. The structure of undergraduate programs differs from country to country and even varies widely within country, so please do ''not'' treat this as a substitute for information about the course structure at a specific educational institution.		The information on this page has been constructed based on an in-depth knowledge of the course structure of a few undergraduate programs and a broad survey of many others. The program surveyed have been based in the United States. The structure of undergraduate programs differs from country to country and even varies widely within country, so please do ''not'' treat this as a substitute for information about the course structure at a specific educational institution.

Vipul: /* Some example university course structures */

2014-02-13T23:43:02Z

Some example university course structures

← Older revision		Revision as of 23:43, 13 February 2014
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	\| [http://math.mit.edu/academics/classes.php Massachusetts Institute of Technology (MIT)] \|\| Semester \|\| 18.01 \|\| 18.02 (multivariable calculus), 18.03 (differential equations), 18.04 (linear algebra) \|\| 18.024, the "Calculus with Theory" course		\| [http://math.mit.edu/academics/classes.php Massachusetts Institute of Technology (MIT)] \|\| Semester \|\| 18.01 \|\| 18.02 (multivariable calculus), 18.03 (differential equations), 18.04 (linear algebra) \|\| 18.024, the "Calculus with Theory" course
	\|-		\|-
	\| [http://math.berkeley.edu/programs/undergraduate/minoring-mathematics University of California, Berkeley] \|\| Semester \|\| 1A and 1B \|\| 53 and 54 \|\| ~~None available (~~?)		\| [http://math.berkeley.edu/programs/undergraduate/minoring-mathematics University of California, Berkeley] \|\| Semester \|\| 1A and 1B \|\| 53 and 54 \|\| ?
	\|}		\|}