Patterns in Environmental Math

Math 12, Section 1


MWF 1.10-2pm, DGH 216



Taught jointly with Drs. McGowan and Schwartzman



Department of Mathematics

Course: Patterns in Environmental Math (3 credits)


COURSE DESCRIPTION: This course teaches some basic concepts of mathematics through applications from environmental science, in particular the science of energy, while providing the necessary background on energy related issues. It will use online (Blackboard) assignments using Tegrity, guest lectures, one field trip and a course project.


REQUIRED TEXT:  Martin Walter, “Mathematics for the Environment.”



1.    To enable the student to apply his or her knowledge of linear, quadratic, exponential, and logarithmic functions and their graphs, basic probability theory and statistics, and arithmetic and geometric sequences to real world problems concerning energy and the environment.

2.    To gain the background knowledge needed to describe and discuss alternative energy theory and applications sufficiently to be prepared for training in careers in the solar and wind energy industries.


STUDENT LEARNING OBJECTIVES:  On completion of the course, students should be able to

Š      Interpret and use graphs of polynomial, exponential and logarithmic functions arising in real world situations involving energy and the environment.

Š      Interpret and apply probability theory to simple questions related to the environment.

Š      Apply the compound interest formula for geometric sequences to the problem of financing energy projects.

Š      Explain the cause of about climate change and its effect on the environment

Š      Describe the basic math and science of energy conservation, solar and wind energy production, and demonstrate simple computations involving these principles.


PREREQUISITE:  A satisfactory grade in College Algebra I.


Instructors: Jill McGowan, David Schwartzman and Sankar Sitaraman



                                                2 one hour exams 15 % each                               Total  30 %

                                                Assignments                                                             Total  25 %

                                                Feedback on class activities                                 Total  5   %

                                                Final Exam 20 pts                                                    Total  20 %

                                                Seminar presentation                                            Total  20 %

                                                                                                            Grand Total              100 %



Academic Code of Student Conduct (please see Howard University handbook):
No copying, unauthorized use of calculators, books, or other materials, or changing of answers or other academic dishonesty will be tolerated. Cheating will not be tolerated. Anyone caught cheating will receive an F for the course and may be expelled from the university.

AMERICAN DISABILITIES ACT: Howard University is committed to providing an educational environment that is accessible to all students. In accordance with this policy, students in need of accommodations due to a disability should contact the Office of the Dean for Special Student Services (202-238-2420, for verification and determination of reasonable accommodations as soon as possible after admission and at the beginning of each semester as needed.

Statement on Interpersonal Violence: Howard University takes sexual assault, dating violence, domestic violence, stalking and sexual harassment seriously. If a student reveals that he or she needs assistance with any of these issues, all responsible employees, including faculty, are required to share this information with the University Title IX Office (202-806-2550) or a student can be referred for confidential services to the Interpersonal Violence Prevention Program (IVPP) (202-238-2382) or the University Counseling Services (202-806-6870). For more information, please go to www.CampusSafetyFirst.Howard.Edu

             Syllabus, including guest speakers and course projects


Some topics are to be covered in a learning module. They are indicated by a (T) for Tegrity (on Blackboard) module and HW for a homework assignment it is marked by (HW).




MIT open course “Physics of Energy.”

Van Jones “Green Collar Economy”

Self-directed learning modules created by the instructors using Tegrity (on Blackboard).

Course format:

The approximately 40 class meetings will be divided as follows:

3 exams

2 guest lectures

1 field trip

32 lectures (see individual topics for distribution of lectures among us)

2 student seminar days (in class).


Course material:


Part 1. Ecosystems and climate change (8 lectures + 1 guest talk )


Guest lecture 1: Expert on ecology & climate change

(Possibly Mark Chambers, Associate Director for Sustainability, DC General Services department).


Aim: To provide background information on the environment and climate change using applications of basic math concepts.



1.    Feedback loops: Edison's Algorithm: Listening to Nature's Feedback. (lecture to be accompanied by (T) module on feedback and renewable energy)

2.    Effect of human activities on ecology, effect of ecological disturbances on human society: Suburbia's Topology (accompanied by (T) module on effect of fossil fuels on urban environment).

3.    Mathematics and basic science of resource availability, energy needs : Hubbert's Peak and the End of Cheap Oil ( accompanied by (HW) assignment on Resource Wars: Oil and Water ).

4.    Energy and climate change : The CO_2 Greenhouse Law of Svante Arrhenius (accompanied by (HW) or (T) radiative energy forcing law).

5.    Probability and statistics laws and properties (accompanied by (T) module on probability and climate change).



Part 2. Basics of energy conservation (10 lectures )


Aim: Building on the foundations from part 1, we outline the practices that help to conserve energy and hence protect the environment.




1.Energy conservation. Mathematics and science of energy use: Energy and the First Law of Themodynamics, Entropy and the Second Law of Thermodynamics, Measuring Entropy, Applications of the Second Law of Thermodynamics.

2. Sustainability practices, recycling and zero waste movement, nature conservation, overview of technology available for energy efficiency for homes and cities. (accompanied by (HW) : research campus building energy use and survey energy efficiency and sustainability measures on campus, possibly in collaboration with Office of Sustainability)

Part 3. Basic math and science of wind, solar and biofuels

(16 lectures + 1 guest talk +  one field trip)



Guest lecture 2: Expert from solar industry / solar installer

( Possibly Joshua Rodgers of Sustainable Energy Systems)


Field trip: Local Solar / Wind installation



1.    Energy: calculation of energy and power from various sources (accompanied by (T) module on units of energy and conversion)

2.    Amount of Solar Energy

3.    Solar Energy Methods

4.    Photovoltaics and solar thermal: overview of technology, basic data on efficiency and capacity of various systems.

5.    Geometric sequences, compound interest formula and its applications.

6.    Study of cost and financing options for solar and wind.

7.    Net Primary Productivity, Soil, Biofuels, and the Super Grid.

8.    Overview of other technology available for renewable energy generation, such as biomass, geothermal, tidal.



Part 4. Course project (to be developed jointly) and Seminars.


Students will be divided into research groups. Each group shall develop in consultation with instructors a small, local project that can be completed within the semester, related to or originating from one of the lectures, learning modules or assignments. Development should start in the second month of the semester and continue concurrent with course. Once project is completed, the student group will give a seminar presentation to the class describing the project.