10 Sep Writing Assignments/Technology Assignments
Writing Assignments/Technology Assignments
You will complete a total of eight writing/technology assignments throughout the semester. You can
choose these from the list below. You can all be writing assignments, or they could all be technology
assignments or some can be writing and some can be technology. The dues dates are listed in the
syllabus.
Writing Assignments Requirements
Each writing assignment is worth 20 points should include the following sections:
Background (3 points): This is a discussion of how the non-mathematical and mathematical portions of your topic fit
together. You might include a historical background of the topic, definitions of terms, the discrete mathematics ideas
that are addressed (e.g. induction, logical fallacy, etc.), and some explanation about why these ideas were useful.
Examples (10 points): In most of your writing assignments you are asked to discuss and describe an aspect of discrete
mathematics. Give two of three examples or techniques of the topic under discussion.
Give general information and also specific examples of the topic.
Bibliography (2 points): List the references you used to complete this report. Just list title and author for any books and
articles you used. You should also include a list of people that you consulted or any other form of help that you received.
For example, you might obtain some of your information from the internet; in this case, you could include the
website. You’ll need at least one book or article as a reference, preferably two, and a total of at least two references.
You’ll notice that there are still 5 points unaccounted for. The remaining 5 points are for style: clarity, neatness, flow,
design, organization and creativity–it’s important to be able to communicate your ideas.
Note: you don’t have to put your report in the precise order given above. You may prefer to use the assigned problems
to illustrate how the ideas of the subject fit together with the mathematical ideas that you will be using, in which case
Background and Examples would be interwoven. Just make sure that these aspects appear in your report.
Technology Assignments Requirements
Each technology assignment is worth 20 points should include the following sections:
Background (5 points): This is a written paragraph of how the non-mathematical and mathematical portions of your
topic fit together. In other words, you need to talk about what you needed to know about your topic in order to solve
the problems and how discrete mathematics fits into the picture. So you might include the definitions of terms, the
discrete mathematics ideas you used (e.g. induction, logical fallacy, etc.), and some explanation about why these ideas
were useful.
Solution (15 points): In most of your technology assignments you are asked to write a program to solve a problem. Copy
and paste your code in a Word document and annotate each section of the code with explanation of what are you doing
in each section. Include a screen shot of the output of the program. If you are using EXCEL, include the excel file as a separate attachment.
Writing and Technology assignments will be submitted in Canvas and checked with SafeAssign. Make sure to submit
your own work and give written explanation using your own voice. Compile your work in one document and save it in
pdf format and submit it by clicking on the assignment title.
Writing Assignments:
Combinatorics:
1. Describe some of the earliest uses of the pigeonhole principle by Dirichlet and other mathematicians
2. Discuss the importance of combinatorial reasoning in gene sequencing and related problems involving
genomes.
3. Describe the different models used to model the distribution of particles in statistical mechanics,
including Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac statistics. In each case, describe the
counting techniques used in the model.
Logic:
4. Discuss logical paradoxes, including the paradox of Epimenides the Cretan, Jourdain’s card paradox,
and the barber paradox, and how they are resolved.
5. Describe some of the techniques that have been devised to help people solve Sudoku puzzles without
the use of a computer.
6. Describe how fuzzy logic is being applied to practical applications.
Proofs and Induction:
7. Look up some of the incorrect proofs of famous open questions and open questions that were solved
since 1970 and describe the type of error made in each proof.
8. Describe the origins of mathematical induction. Who were the first people to use it and to which
problems did they apply it?
Algorithms:
9. Describe six different NP-complete problems.
10. Describe the historic trends in how quickly processors can perform operations and use these trends
to estimate how quickly processors will be able to perform operations in the next twenty years.
11. Describe what is meant by a parallel algorithm. Explain how the complexity of parallel algorithms can
be measured. Give some examples to illustrate this concept, showing how a parallel algorithm can work
more quickly than one that does not operate in parallel.
Relations and Functions:
12. Discuss the concept of a fuzzy relation. How are fuzzy relations used?
13. Describe how equivalence classes can be used to define the rational numbers as classes of pairs of
integers and how the basic arithmetic operations on rational numbers can be defined following this
approach.
Recursion:
14. Describe a variety of different applications of the Fibonacci numbers to the biological and the physical
sciences.
15. Explain the different ways in which the Encyclopedia of Integer Sequences has been found useful.
Also, describe a few of the more unusual sequences in this encyclopedia and how they arise.
16. When are the numbers of a sequence truly random numbers, and not pseudorandom? What
shortcomings have been observed in simulations and experiments in which pseudorandom numbers
have been used? What are the properties that pseudorandom numbers can have that random numbers
should not have?
Number Theory:
17. Describe the history of the Chinese remainder theorem. Describe some of the relevant problems
posed in Chinese and Hindu writings and how the Chinese remainder theorem applies to them.
18. Describe the algorithms that are actually used by modern computers to add, subtract, multiply, and
divide positive integers.
19. Show how a congruence can be used to tell the day of the week for any given date.
Graph Theory:
20. Discuss the applications of graph theory to the study of ecosystems, to sociology and to psychology.
21. Explain how graph theory can help uncover networks of criminals or terrorists by studying relevant
social and communication networks.
22. Describe some of the strategies and algorithms used to solve the traveling salesperson problem
Boolean Algebra
23. Describe some of the early machines devised to solve problems in logic, such as the Stanhope
Demonstrator, Jevons’s Logic Machine, and the Marquand Machine.
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