Bronx Community College
of the City
University of New York
Department of Mathematics and Computer Science
---------------------------------------------------------------------------------------------------------------------
MTH
37 -- ELEMENTS of CALCULUS and STATISTICS for Biology Students
4 credits, 4 hours per week
COURSE SYLLABUS
PREREQUISITE: MTH 31 with
grade C or higher or placement by the
department
TEXT: Mathematical Methods for
the Life Sciences, by E.H. Grossman, City College
of New
York, customized edition.
Additional Text: An Introduction to the Mathematics of Biology, by Yeargers, Shonkwiler,
Herod, BirkhŠuser, 1996.
CALCULATORS: TI-83/83+ (or equivalent) is required. Some classes
will meet in a computer lab
Course Grading
Policy:
1.
Each of two (2) Class Exams (tentatively, during the
second week of October and the fourth week of November) is worth 15% of your
final course grade.
2.
Home assignments are worth
15% of your final grade. Attendance will be taken at every class during the
first minute of the class.
3.
Written team project, due during the first week of December, is worth
15% of your final grade.
4.
The Final Exam is worth 40%
of your final course grade IF the
Final has been passed by achieving a 60 or higher. Failing the Final Exam implies failing
the course.
Course Objectives:
Learn basic concepts and
results that form the background of Ordinary Differential Equations and
Statistics and their applications, such as models of exponential growth and
logistical models, steady-state solutions and the stability of solutions of
simplest ordinary elementary differential equations and systems of equations,
probability rules, data classification, graphical presentation of statistical
data, measures of central tendency, regression analysis, examples of discrete
(binomial) and continuous (normal) distributions, introduction to construction
of confidence intervals and hypothesis testing. Learn more advanced topics such
as the Law of Large Numbers and the Central Limit Theorem that require some
calculus background. All theoretical material will be preceded by model
problems and will be illustrated, accompanied, and followed by solution of many
problems. At the end of this course, the students are supposed not only to know
certain definitions, theorems, etc., but also to be able to apply these to
specific statistical projects. MS Excel spreadsheets are used to illustrate
some of the mathematical and especially statistical topics. The students will
become acquainted with the statistical software in Excel.
General Remarks:
Students should study, at the very least, THREE hours at home
after each hour in the classroom. At home you should look through your class
notes, read the assigned sections from the text, and only after that (not
before!) start to solve problems. At the beginning of every class some time is
devoted to answering the studentsÕ questions. Prepare your questions BEFORE the class,
not after the class started.
Punctuality. As a matter of common courtesy, arrive in class on time (if you are not early, you are late).
Integrity. The BCC Academic Integrity Policy is the governing
policy document. Every student is responsible for knowing its implications and
observing them. No cheating is tolerated.
COURSE OUTLINE
|
Section |
Topic |
Home Work |
Time (in hours) |
|
1.1-1.2 |
Review of Calculus. Derivatives and
antiderivatives of exponential and
logarithmic functions |
|
4 |
|
Appendix A |
Intro. to
Excel |
|
1 |
|
2.1-2.2 |
Intro. To ODEs, separable
ODEs |
|
3 |
|
2.3 |
Exponential growth |
|
1 |
|
3.1-3.2 |
EulerÕs method |
|
2 |
|
4.2 |
Steady state solutions |
|
1 |
|
4.3 |
Geometric analysis |
|
2 |
|
4.4 |
Stability |
|
1 |
|
5.1-5.2 |
Malthus model, harvesting |
|
2 |
|
5.3 |
Logistic model |
|
1 |
|
6.1-6.2 |
Systems of ODEs |
|
2 |
|
6.3 |
Steady states, Phase plots |
|
1 |
|
6.4-6.5 |
Stability; application to
epidemics |
|
2 |
|
7.1-7.2 |
Histograms |
|
1 |
|
7.3-7.4 |
Measures of central
symmetry and spread |
|
2 |
|
7.5-7.6 |
Box plots, five-point summery,
estimation |
|
1 |
|
8.1-8.3 |
Correlation coefficient |
|
2 |
|
9.1-9.3 |
Method of least squares;
prediction |
|
2 |
|
9.4-9.5 |
More on regression |
|
Time permitting |
|
10.1-10.2 |
Intro. to
probability |
|
1 |
|
10.3-10.4 |
Counting |
|
2 |
|
10.5 |
Probability rules |
|
2 |
|
11.1-11.3 |
Mutually disjoint and
independent events. Conditional probability and BayesÕ theorem |
|
2 |
|
12.1-12.4 |
Genetics; Hardy-Weinberg
theorem |
|
Time permitting |
|
13.1-13.2 |
Discrete random variables |
|
2 |
|
13.3 |
Binomial distribution |
|
2 |
|
13.4 |
Poisson distribution |
|
1 |
|
14.1-14.2 |
Continuous random
variables; uniform distribution |
|
1 |
|
14.3-14.4 |
Normal distribution |
|
3 |
|
14.5 |
Normal approximation to
binomial distribution |
|
2 |
|
15.1-15.3 |
Inferential statistics;
confidence intervals (large samples) |
|
3 |
|
15.4 |
Small samples (t
distribution) |
|
1 |
|
|
|
|
Total: 53 |
3 hours left for
reviews, tests, etc.
A.
Kheyfits:
03/22/2009; Revised 04/10/2011