the following information is tentative and will be updated during the semester.

projects are only for students enrolled in 5383. for the project, you should learn about a topic related to the course material, and write a report and give a presentation on this topic. your topic must be approved in advance, and must contain a significant amount of mathematical and/or programming content. the report and the presentation will be graded separately, and each is worth 50% of your project grade.

you may do your project individually or with a partner. (the partner should also be in 5383--no ringers!). if you choose to work with a partner, then i will expect more substance to your project, with a description of what each person contributed, and both individuals still need to give a presentation.

deadlines

• 3/23-3/27: submit a project proposal - via email, send me roughly a paragraph explaining what you'd like to do for your project. if you want to do your project with a partner, each of you should still send me separate emails, and say who you want to work with.
• mon 4/13: turn in a draft/detailed outline to me via email. i will plan to give you feedback by the end of the week. you may submit this earlier if you want feedback earlier.
• 4/20--4/29: give a presentation (10-15 min per person). we will discuss scheduling in april, but if there is a certain day you want to present, feel free to
• th 5/7: submit your final written project (you may hand in a print-out at the final exam period or email it to me by the end of the day, or anytime earlier) AND the slides from your presentation

suggested ideas for projects

• classical ciphers: double transposition and nihilist ciphers like VIC
• crypography in world war i
• crypography in world war ii
• nist standards: des/aes
• primality testing
• factorization algorithms
• elliptic curve crypography
• digital signature schemes/pgp
• cryptocurrencies (e.g., bitcoin)
• random number generation in cryptography
• modern password security (protocols, salting, hashing)
• error-correcting codes
• shannon information theory
• data compression
• ...

report guidelines

the main general guideline is that you should write the report like a professional mathematical exposition. here are a few of examples of mathematical exposition:

• my notes on sums of squares, sums of cubes and modern number theory (structurally, that exposition is longer than i'm expecting from you, and you don't need an abstract or table of contents, though you can include them if you want; of course topically this is not about "applied algebra")
• carmichael numbers and pseudoprimes by graham jameson (topically relevant, but for your project, i'd like some exposition about the relevance and import of pseudoprimes to cryptography and rsa)
• the fifteen puzzle (and rubik's cube) by keith conrad (of course, topically this is not a great fit, though is about "applications" of algebra, and for your project, i'd like expect more of an introduction)

structural requirements/guidelines:

• your name and project title should be at the top or on a separate title page, your choice
• the write-up should consist of an introduction, main text, references and if appropriate appendices (for code, supplementary tables, etc).
• the introduction should clearly introduce your subject and summarize what you are doing in the project.
• it is a good idea to split the rest of the main text into sections, according to subtopics. the text might have a conclusion section at the end---whether it makes sense to do this depends on your project, but it's probably a good idea most of the time.
• label/name theorems, examples, etc and use those labels/names when you refer to them later (as a general practice, you don't necessarily have to do this every time)
• when appropriate for facts, results, ideas, etc., make references to quality sources (this does not typically include things like wikipedia, reddit, blogs, etc--it means things like textbooks and professional articles). present the references as a list at the end of the main text, like a standard math paper (e.g., see my expository notes above--you don't have to follow the exact formatting). you should cite all of your main sources, and all or the references in the reference list should be referred to in the main text when you are using them. and any quotations (copied text), reused figures, etc. should clearly delineated and sourced. there is no strict requirement on the number of references you need, but it's better if it's more than 1 or 2 sources.
• the format for the intro + maint text should be standard 12pt font, single-spaces 1-inch margins.
• the length of the intro + main text should be roughly 10-15 pages. (do not count references, figures, code, etc. it's fine to have figures in the main text, but i don't want to see your main text ending on p. 10 if 5 of the pictures in between are just pictures. i also don't want to see 5 pages of quotes--remember originality.)
• any code which you wrote or supplementary data should be included at the end as appendices. if you use someone else's code, that's fine, just reference their code appropriately. you're also welcome to use various python modules etc., or languages that aren't python, but you shouldn't expect that i will know the language you are using. however it may make sense to include snippets of code or pseudocode in the main text, if you are talking about algorithmic/computational aspects.

general guidelines:

• imagine your audience for the report consists of your fellow students in the class. write roughly at this level, though you may use slightly more advanced standard mathematics without explaining (e.g., things covered our 4000 level intro to abstract algebra course). certainly you shouldn't assume i know everything you've studied in preparing for this project. (possibly i know it quite well, and possibly not, depending on your project; but you will be graded in part on how clearly you explain your material to an audience similar to your classmates.)
• define notation and clearly define concepts/mathematical definitions that you introduce which we have not already covered in class.
• you need to show off some analytical abilities in the project, so you should write up things like proofs of key results (when possible); working out details of examples; clearly explaining/analyzing algorithms; writing your own nontrivial code; and clear logical explanation of how different ideas fit together. now i don't expect your project to have all of these aspect, but at least 1 or 2 of them should be a significant component of your project. if you are following proofs or examples from other sources, you should cite them, but write them up in your own words. however, for examples, if feasible i'd like you to try to work out your own examples to really understand the material.
• the writing should be reasonably professional, like the example expositions above, but it can be a bit casual. e.g., you can write in the first person if you want. feel free to add more informal or meta comments in footnotes (e.g., "i tried to figure out if the converse of this theorem is true, but couldn't. i still think it should be true because...")
• i suggest, but do not require, that you write your report in latex, or some tex variant.
• if you have questions as you're working on your project, either about the material or references, or what i'm looking for, please ask.
• submit your report as a single pdf file, by email to me, by the appointed day

presentation guidelines and suggestions

your presentation should be:

• 10-15 minutes in length. (expect that you may get asked 1 or 2 questions during your presentation, and then a couple at the end.)
• present with computer "slides". while you may use the board to quickly sketch out something or help answer a question, you should not be spending most of your time writing on the board. (note: you are expected turn in your slides to me together with your written report.)

• make slides using latex+beamer or powerpoint
• have a title slide with a poignant title and your name(s)
• each slide should be easy to read: generous font size, highlight main ideas, and illustrative pictures are always nice
• except for the title slide, spend more than 10 seconds on each slide. if you go through your slides too quickly, the audience will not have time to absorb what is on each slide. (corollary: do not have 100 slides)
• you don't need to talk about everything you did for your project in your presentation. in fact, you shouldn't have time for this. focus on the most interesting/important aspects.
• your presentation should have 1 or 2 main points. for most topics, it's suitable to start with a motivating question, which you will at least partially answer by the end. emphasize the problem at the beginning, and the answer at the end. some speakers outline their talk in advance so the audience knows where they're going, but it's perhaps unnecessary for a 15 minute presentation. (this structure is similar to what I expect for a write-up.)
• do you enjoy teachers who just read out of the book? if not, don't just read your slides word for word either. slides should not be a transcript of what you're going to say, but visual highlights/reminders to help the audience focus on and understand what you're talking about. if you want you can have separate notecards to remind yourself what you want to say about each slide. but again, don't read the notecards verbatim.
• the audience for this presentation is your fellow students, not me. make it understandable for them, so they can learn something. your project write-up is directed to me, so you can say more advanced things there.
• practice your talk at least 2-3 times, and time these. the first time should be just to figure out exactly what you will say/how to explain things and get a general sense of your timing. then edit things in or out if you need to, and try timing it again. repeat until you're confident you can finish in time.
• anticipate likely questions from the audience so you can prepare anwsers and sound like a genius when you answer them skillfully. or pre-emptively answer them in your presentation.
• did I say make sure you can finish in time? a minute over is forgivable. five is not. keep an eye on the clock, and figure out how to shortcut to your thrilling conclusion if you are running short on time.
• thank your audience at the end.