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Saint Michael's College is a private, residential liberal arts Catholic college. The 440-acre (1.8 km2) campus is located in Colchester, Vermont. It was founded in 1904 by the Society of Saint Edmund, a French order of Catholic priests.
More information: http://en.wikipedia.org/wiki/Saint_Michael%27s_College
Course Objectives
Course ObjectivesRead Mathematics Mechanical Proficiency |
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Optimization
OptimizationLocate the “optimizing adjective”, a word such as: largest, least, minimal, etc. The noun this adjective modifies will be your “key word”. Assign it a variable name, e.g. A. Write an equation for this key word: A = some stuff (usually involving at least two other letters, say x and y). This is your principal equation. Look for some other information in the problem that lets you write an equation using the other letters. This is your constraint equation. Write it down and solve for either x or y . Replace the value you solved for (say y) in the principal equation to get a function of one variable, A(x). Use calculus to find the max/min of A(x): Find A’(x), set it equal to 0 and solve. If necessary, use the second derivative test to see if the critical point you found is a max or a min. Re-read the problem to see whether they want x, A(x), (x, y ) or e.g. ‘the dimensions’. |
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Related Rates
Related RatesThere will be a rate you know, say dA/dt =-2. There will be a rate you want to know, say dB/dt, when… (need to be given some information here, e.g. “when B=4”). Write an equation relating A and B (using formulas from the flyleaf or similar triangles, etc.), e.g. A2 + B2 = 25. Differentiate both sides with respect to t: 2A dA/dt + 2B dB/dt =0. Figure out what all the values are except the rate you want. E.g. here B=4, so from A2 + B2 = 25, it follows that A=3. Plug these values in and solve for the rate you want: 2*3 * (-2) + 2*4* dB/dt =0, so dB/dt =-2/3. |
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Tucker, Applied Combinatorics, Sec. 3.5, Jo E-M
Tucker, Applied Combinatorics, Sec. 3.5, Jo E-M“Big O” Notation We say that a function is if for some constant c, when n is large. For example, is since for n > 3. This is described by saying that is ‘on the order of’ . Big O notation calls attention to the part of a function that grows the fastest, so gives a simple estimate of how many steps are required for an algorithm to run. |
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Thermodynamics
Thermodynamics |
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Educating our ELLs Ideas to help teachers educate
English Language Learners
Mary Westenfeld
Addison Northwest Supervisory Union
Educating our ELLs Ideas to help teachers educate English Language Learners Mary Westenfeld Addison Northwest Supervisory Union |
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Math for ALL Students: Walking the Walk
Math for ALL Students: Walking the Walk |
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3.3 Spanning Trees Tucker, Applied Combinatorics, Section 3.3, by Patti Bodkin and Tamsen Hunter
3.3 Spanning Trees Tucker, Applied Combinatorics, Section 3.3, by Patti Bodkin and Tamsen Hunter |
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Network Flows Michael Duquette & Whitney Sherman
Network Flows Michael Duquette & Whitney ShermanTucker, Applied Combinatorics, Section 4.2a, Group G |
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Effective Presentations
Effective PresentationsQ: How many of you have given a presentation before? How did it go? Q: Who feels it could have gone better? Why? Q: What is the worst fear? Speakers have a responsibility to their audience to be effective! |
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Tucker, Applied Combinatorics, Sec. 4.3, prepared by Jo E-M
Tucker, Applied Combinatorics, Sec. 4.3, prepared by Jo E-MSome Definitions X-Matching Maximal Matching A set of independent edges Edges only between X and Y X Y All vertices in X are used The largest possible number of edges Note: an X-matching is necessarily maximal. Bipartite Graph Matching |
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Parents Are the Secret Ingredient Suggestions for Helping Your Child Do Well in School
Parents Are the Secret Ingredient Suggestions for Helping Your Child Do Well in Schoolby Yvonne Sonoda MATESOL Candidate Saint Michael’s College, May 2008 |
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Chapter 4 Network Algorithms Section 4.1 Shortest Paths
Colleen Raimondi
Chapter 4 Network Algorithms Section 4.1 Shortest Paths Colleen Raimondi |
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Tucker, Applied Combinatorics, Sec. 3.2,
Tucker, Applied Combinatorics, Sec. 3.2,Here the paths would be: (A-B), (A-B-D), (A-B-E), (A-C) and (A-C-F) A B C D E F Important Definitions Enumeration: Finding all of the possible paths in a rooted tree that begin at the root, or the solutions that that path represents. This means finding the unique path from the root to each internal vertex and leaf. |
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How Big is the Universe?
How Big is the Universe?The observable Universe is greater than 12 x 109 light years in radius. (12 x 109 years)(365 days) (24 hr) (60 min) (60 sec) (3 x 108 m ) ( 1 km ) ( year ) (day ) ( hr ) ( min ) ( sec ) ( 103 m ) = 2 x 1021 km !!!! (20000000000000000000000 km) That’s big! Photo of Universe not available. (light travels 1.6 x 1011 km: 1600000000000 km in a year) |
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The Kent Study of Library Use
The Kent Study of Library UseAcquisitions of books: 40 percent did not circulate in 7 years. When a book does not circulate within the first 6 years of ownership, the likelihood of its ever being borrowed is: less than 1 chance in 50. --(Univ. of Pittsburgh) 1977 |
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The Mathematics of Golf By
Jennifer Morgan
The Mathematics of Golf By Jennifer Morgan |
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