Finite Mathematics, Section 4
Math 139
Spring 2004
Instructor: Prof. Dr. rer. nat. Henri Schurz
Time: MWF 10:00am - 10:50am, Location: WHAM 306
Office Hours: MWF 9:00am - 9:50am, 11:30am - 12:30pm
(Last Update: 04/13/04)
Old sample exams and solutions are available from
the central departmental webpage on courses!
Textbook:
Finite Mathematics: An applied approach, 7th Edition.
by M. Sullivan, Prentice Hall, Boston, 2000.
Read this
Without Tears:
WHAT IS EXPECTED OF YOU
(From "Teaching at the University Level" by Stephen Zucker, Notices Amer.
Math. Soc. 43 (1996), p. 863):
1. You are no longer in high school. The great majority of you, not having
done so already, will
have to discard high school notions of teaching and learning and replace
them by university-level
notions. This may be difficult, but it must happen sooner or later, so
sooner is better. Our goal is
more than just getting you to reproduce what was told you in the classroom.
2. Expect to have material covered at two to three time the pace of high
school. Above that, we
aim for greater command of the material, especially the ability to apply
what you have learned to
new situations (when relevant).
3. Lecture time is at a premium, so it must be used efficiently. You cannot
be "taught" everything
in the classroom. It is YOUR responsibility to learn the material. Most of
this learning must
take place outside the classroom. You should be willing to put in two hours
outside the classroom
for each hour of class.
4. The instructor's job is primarily to provide a framework, with some of
the particulars, to guide
you in doing your learning of the concepts and methods that comprise the
material of the course. It
is not to "program" you with isolated facts and problem types nor to monitor
your progress.
5. You are expected to read the textbook for comprehension. It gives the
detailed account of the
material of the course. It also contains many examples of problems worked
out, and these should
be used to supplement those you see in the lecture. The textbook is not a
novel, so the reading
must often be slow-going and careful. However, there is the clear advantage
that you can read it
at your own pace. Use pencil and paper to work through the material and to
fill in omitted steps.
(till here: extracted from Joe Mashburn (Uni Dayton)/
joe.mashburn@udayton.edu)
6. Do not expect that exam problems are exactly the same as in homework
problems. Homework problems should be understood to strengthen and to
improve
your knowledge on subject related issues.
7. Work with your TA's as much as you can and form study groups if
necessary, ask subject related questions, and be active.
8. Read further additional literature (Do not stick to course material
completely!). The professors can always give you more literature hints.
9. Make always written notices what the instructor tells you about the
subject, work through your course notes after the lectures promptly and continuously.
10. We all expect mutual respect, polite, correct, honest and
sincere personal behaviour on student's and instructor's side as it
should be common among human beings.
(These are my main 10 principles for success in academic studies!)
Course
Description: This course is the first treatment
of major mathematical, but calculus-oriented topics of sets, counting,
elementary probability, line sketching, linear systems of equations,
matrices, linear programming and the simplex algorithm.
It is meant to be a basic introduction for beginners into something
what is called "finite math" somewhere.
Prerequisites
and Development of Contents:
This course should be accessible to any student with a $C-$ in
College Algebra / Precalculus or placement exam. However, I strongly advice you to review
your knowledge which you should know from high school math in your
previous carrier. I will always assume that you profoundly know the
facts from that part, including most important standard formulas.
The content of this course itself should very nearly coincide with that of our
textbook, running through chapters 6, 7, 1 and 2.
I am not perfect. However, be sure that I
will do my very best to please you and your expectations.
Readings,
Problem Sets, Exams:
Readings and problem sets will be from the text and my manuscript, and
it will be assigned in classes and perhaps additionally published at
my homepage. Exams will cover all material covered in the lectures,
recitation classes and/or the readings. The authors seem to
have put some fair effort into their presentation from very practically
oriented point of view, and her approach is probably quite different
from what you've seen before (hopefully not). Thus, I really encourage
you to read the book as lectures advances and to be aware of the
symbol page of our course (see below).
Exam
Dates:
- Midterm I: Friday, February 20, 2004 (in class)
- Midterm II: Friday, March 26, 2004 (in class)
- Midterm III: Friday, April 23, 2004 (in class)
- Final: Lawson 121, May 3, 10:10am-12:10pm, 2004 (to be checked)
Grading Strategies - Grade Distribution:
- 20 % Homeworks & Quizzes, 40 % Midterms (Total Sum), 40 % Final Exam
- Deviation guideline: Except for very
well-documented cases, there is only such an overall grade
possible which differs from the grade result of final exam
at most about one grade.
- Your scores from homeworks & quizzes are recorded by your TA.
The score of the final exam is also evaluated according to the
gradeline meeting on total grade distribution of all students after the final
date. Thus, your results in the midterm and final exams will rule over the
remaining portion of quizzes and homeworks.
Course
Syllabus (To be uploaded, Last Update: 01/12/04) - You will need an utility
like ghostview to read it!
Please, note you need ghostview to read the postscript files after
downloading! See http://www.cs.wisc.edu/~ghost/index.html for more software
product information.
Course
Symbol Page (Last Update: 01/12/04) - You will need an utility
like ghostview to read it!
Remarks for the Prerequisites and First Week:
Please, review problems from college algebra and precalculus. You should know the
most important mathematical symbols and some grasp what is a function all about.
Remarks for the 1st Midterm Exam:
Please, review your notes and sections 6.1. - 7.5., 8.1. The midterm I is of
multiple choice. Midterm I will contain 20 problems, each graded with a
total of 5 points. The main goal is to check your capability of
learnt finite math techniques. In particular, you should be sure in
set notions and operations, counting (multiplication principle, permutations,
combinations, binomial theorem), probabilities (sample space, probability
space, events, axioms of probability, independence, conditional probabilities,
Bayes formula). No books, no notes, no
tables, no calculators at all, no notebooks are permitted (pocket scientific
calculators wouldn't help you much anyway).
You should know all formulas which appeared in class and blackboard notes
(consistent with the textbook), i.e. you also should be able to
understand and work with them. Math is not just formulas! Prompt mathematical
thinking will be tested.
Practice Test I (for a total time of lesser than 11 minutes):
- 1. Compute C(9,2)
A = 9 | B = 2 | C = 36 | D = 18 | E = 9!/2!
- 2. Calculate P(9,7)
A = 9 | B = 7 | C = 63 | D = 9!/7! | E = 9!/2!
- 3. Calculate the probability P(A ^ B) with P(A)=0.25,
P(B)=0.85, P(A u B) = 0.9
A = 1/5 | B = 0.25 | C = 1 | D = 0.85 | E = 0.6
- 4. What is the probability of having the sum of the faces of two fair dice
is exactly equal to 6 if tossing of them is independent (each one time)?
A = 1/36 | B = 5/36 | C = 1/2 | D = 1/6 | E = 4/36
- Correct answer-sequence is C-E-A-B.
Remarks for the 2nd Midterm Exam:
Please, review your notes and sections 8.1.-8.2., 1.1.-1.3., 2.1.-2.3. The midterm II is
of multiple choice. Midterm II will contain 20 problems, each graded with a
total of 5 points. The main goal is to check your capability of
learnt finite math techniques. In particular, you should be sure in
probabilities (sample space, probability space, events, axioms of probability,
independence, conditional probabilities, Bayes formula, Bernoulli trials,
binomial probabilities). No books, no notes, no
tables, no calculators at all, no notebooks are permitted (pocket scientific
calculators wouldn't help you much anyway).
You should know all formulas which appeared in class and blackboard notes
(consistent with the textbook), i.e. you also should be able to
understand and work with them. Math is not just formulas! Prompt mathematical
thinking will be tested.
Practice Test II (for a total time of lesser than 11 minutes):
- 1. Suppose that one independently throws a fair die n-times. What is
the probability that the face in each throw always is not more than 4?
A: b(n,0,2/3)+b(n,1,2/3)+b(n,2,2/3)+b(n,3,2/3)+b(n,4,2/3) |
B: 1-b(n,6,2/3) | C: 1-b(n,5,1/3)-b(n,6,1/3) |
D: b(n,0,1/6)+b(n,1,1/6)+b(n,2,1/6)+b(n,3,1/6)+b(n,4,1/6) |
E: b(n,0,1/3)+b(n,1,1/3)+b(n,2,1/3)+b(n,3,1/3)+b(n,4,1/3)
where b(n,k,p)=C(n,k) p^k (1-p)^{n-k} denotes the binomial probability with success
probability $p$ and exactly $k$ successes out of $n$ trials.
- 2.
Find the equation of the line which passes through (-2,-5) and which is
perpendicular to y + 1 = - (x-2).
A: y = x - 2 | B: y = x - 3 | C: y = x + 5 | D: y = -x-3 | E: y = -x+2
- 3. Calculate the solution of $2 x + y = 8$ and $2 x - y = -4$.
Which of the answers is correct?
A: x=1, y=2 | B: x=1, y=4 | C: x=1, y= 6 | D: x=4, y=1 | E: x=2, y=-1
- 4. Consider the upper triangular system $x+y+z=1$, $y+z=1$, $z=1$. What
can you say about its solution (x,y,z)?
A: no solution at all | B: infinitely many solutions | C: two distinct solutions |
D: one unique solution | E: there are at least two solutions
- Correct answer-sequence is A-B-C-D.
Remarks for the 3rd Midterm Exam:
Please, review your notes and sections 1.1. - 8.2. The midterm III is not of
multiple choice. It contains 5 problems. We will test how to calculate
the inverse of a matrix, how to multiply two matrices, how to transform
a LP word problem into a standard max or min form, how to solve a standard
LP problem by a geometric approach and how to do pivoting for the simplex
method applied to standard max problem. Only plain (scientific) calculators
are allowed. No book, no notebook, no notes nor graphical nor progammable calculators
are permitted.
Remarks for the Final Exam:
The final exam is a fairly comprehensive exam for 2 hours.
The topics run from chapters 1 through 8. The final involves
problems on set operations, counting (combinations, permutations),
probability, linear equations, matrices, and linear programming.
Scientific calculators are probably allowed. Other calculators,
notebooks, notes, cheating sheets and books are not permitted.
Bring your I.D. with photo with you.
Current Course Outline (Last Update:
04/13/04, Need to be Revised):
Week 1 : Introduction, 6.1.-6.3.
Week 2 : Martin-Luther-King Day, 6.4.-6.5.
Week 6 : 8.1., Review, Exam I
Week 11: 2.4., Review, Exam II
Week 15: 4.3.-4.4., Review, Exam III
Week 16: Review for Final Exam
Remarks for Homeworks, Quizzes and Recitation Classes:
The homeworks and quizzes are assigned in classes and are due according to
the syllabus dates thereafter if not otherwise stated in class. The recitation
discussion if needed takes place when the results are returned right after class hours.
The recitation parts are meant to strengthen your knowledge in related
areas touched in lectures. Thus, your active participation is required.
The homeworks and quizzes play an essential role in forming your grade
according to the presented grade distribution.
Homework Assignments (Revised in class, if necessary):
Week XVIb: 2.6.: 2, 10, 26, 34, 54 (due on Friday 04/30/04)
Week XVIa: 2.5.: 4, 12, 44, 48, 50 (due on Monday 04/26/04)
Week XV: 2.4.: 4, 18, 26, 30, 54 (due on Monday 04/19/04)
Week XIV: 2.3.: 6, 18, 24, 34, 46 (due on Monday 04/12/04)
Week XIII: 2.2.: 6, 14, 26, 38, 60 (due on Monday 04/05/04)
Week XII: 2.1.: 6, 12, 18, 24, 42 (due on Monday 03/29/04)
Week XI: 1.2.: 4, 18, 30, 46, 48 (due on Monday 03/22/04)
Week X: 1.1.: 4, 18, 26, 34, 58 (due on Monday 03/15/04)
Week VIIIb: 8.2.: 6, 16, 24, 36, 38 (due on Friday 03/05/04)
Week VIIIa: 8.1.: 10, 16, 28, 30, 36 (due on Monday 03/01/04)
Week VII: 7.4.: 10, 20, 28, 36, 62 (due on Monday 02/23/04)
Week VI: 7.3.: 6, 8, 10, 12, 20 (due on Monday 02/16/04)
Week V: 7.2.: 4, 6, 18, 22, 36 (due on Friday 02/13/04)
Week IV: 6.7.: 4, 6, 12, 16, 18 (due on Friday 02/06/04)
Week III: 6.5.: 8, 14, 16, 20, 28 (due on Friday 01/30/04)
Week II: 6.3.: 6, 10, 12, 14, 22 (due on Friday 01/23/04)
Week I: 6.1.: 12, 14, 16, 18, 24c (due on Friday 01/16/04)