Discrete math is not as easily explained as other mathematical subjects. It is not a single math subject, but a collection of subjects that have in common that they are dealing with "discrete" (not infinitely divisible, not continuous) objects.
MAT 243 is a "buffet" class. We will not study a single subject in depth, but rather get a taste of, which is to mean an introduction to, several important subjects that are all foundational for computer science: logic, set theory, functions and sequences, order of functions, number theory, induction and recursion, counting, probability and relations.
Along the way, we will allude to, and sometimes study, applications to computer science. Logic, of course, is a basic ingredient for programming. So are sets and functions, except in computer science, we call sets "data types". The order of functions helps to understand how much processing power or memory a function will consume. Number theory is the parent of cryptography, the science of encryption and communications security. The math concept of recursion is intimately tied to the programming technique of recursion; and induction is a math tool to prove that a recursive algorithm is correct. To understand best-case, worst-case or average case run times of a program, you may have to use tools from Counting and Probability. Finally, relations are a precise way of talking about.. well.. relations between objects, which is also one of the big themes in computer science and important for databases.
MAT 243 is probably the first real math class you've ever had. You had something in high school that called itself math, but that "math" is to real math like coloring in a coloring book is to painting. It was about blind imitation, memorizing procedures and plugging in numbers. Real math is about understanding, about meta-knowledge: not so much about knowing, but about knowing why we know.
This brings us to the objective that ties our study of the different sub-branches of discrete math together: we want to be able to provethings. In most undergraduate and high school math classes, methods are correct and theorems are true .. because the teacher says so. Because she has a math degree. Because he seems to know what he's talking about and he says the same thing as the textbook. True is whatever will earn you a passing grade in the course.
In MAT 243, just like in MAT 300, MAT 371 and all graduate math classes, we have a higher standard. Mathematical truth is established not by authority, not by emotional persuasion, but by proof. A proof is a logical argument that will convince a reasonable person that some mathematical claim is correct, beyond a shadow of a doubt. It leads the reader or listener from first principles that are recognized as undoubtedly true in a sequence of reasoning steps, each of which is unassailable, to the final statement. At the end of a successfully communicated proof, the reader or listener has an aha experience. She may have accepted the mathematical claim on faith or authority previously, but now she owns this particular bit of math; she knows without a shadow of a doubt that it is true and accurate.
Proofs are where all the action is in real math. Without proofs, math degenerates into high school math - a mindless set of procedures, a collection of "it's true because the teacher said so". High school math is rightfully hated by most students.
Being able to prove a theorem means knowing what makes it work. Understanding math at the proof level gives you the power to modify mathematical tools or to create similar tools of your own. It's the quintessential "that's why they pay me the big bucks" knowledge.
If you are working, or are going to work as a developer, you may be using advanced math in canned form - in the form of pre-made libraries. You don't have to know what the library functions are doing, you just call them, and they work their inexplicable magic under the hood.
But what if a library function returns a mysterious warning or error message? What if it complains that your calling parameters are somehow "illegal"? Then you need to know what's going on under the hood. What's that mathematical condition the documentation tells me is necessary all about, and how do I check for that? If all else fails, you will wish you had the ability to implement a similar function that doesn't have this restriction, or tolerates your exceptional input data more gracefully. For that, you need to understand what makes the function work. That level of knowledge is communicated through proofs.
If you work, or are going to work, as a software developer, you should read You Don’t Need Math Skills To Be A Good Developer But You Do Need Them To Be A Great OneLinks to an external site..In practical terms, all this means that you should expect a steep learning curve. You must take this class seriously if you wish to succeed. Sunday night-only work will lead to almost certain failure, as will cramming the day before the test. The skills you are expected to master here - especially proof writing skill - can only be build through slow and steady cultivation. Proof-writing skill can no more be acquired through last minute cramming than physical fitness or the ability to play an instrument. Mastering proofs requires repeated study and practice.Above all else, don't procrastinate. The time to start working is the first day of class, not the day on which the first set of assignments is due. Due dates are not the dates on which you should be working the problems. They are merely the last dates you are allowed to finish the work.
To do X hours of work on the evening of the due date takes just as much time as doing X hours of work a day earlier. The only difference is that on the evening of the due date, you may not have the ability to do X+1 hours of work, if necessity calls for it.
First things to do: read the syllabus by clicking on "Syllabus" on the left side. It's a lot of information, but it's information you need to know. Only don't read it if you want to fail the class.
After you have read the syllabus, take all the module 0 quizzes - Test 0, the Syllabus Quiz and the College Algebra quiz. Please do this as soon as possible. You will not be able to take exams in the class, including practice exams, until and unless you have passed Test 0 and the Syllabus Quiz.
Course Overview
Learning Goals and Time Commitment Required
The course teaches you about logic, sets, functions, elementary number theory and combinatorics, recursion, and mathematical reasoning, including induction and proof writing. It emphasizes connections and applications to computer science.
More detailed learning outcomes are individually described in each module.
Activities used for instruction and assessment of learning include: watching instructional videos, reading/reviewing the corresponding written presentations, reading the textbook, Ed homework, written homework, quizzes, midterm exams, a final exam and a separate proof writing assignment.
You are expected to spend several hours EACH DAY on this class including weekends. You will almost certainly not succeed if you can only work on the class during the weekends.
The instructor is fully aware of and sympathizes with the time limitations of students who have families and full-time jobs. To accommodate these time limitations, there are no daily quizzes, and exams become available on the night previous to the official testing day.Students subject to real life and career restrictions must accept however that they are still responsible for completing all coursework and putting in the required number of hours. Students who cannot invest the time necessary to complete the coursework should drop the course.
Students are expected to take note of examination dates (midterms and final exam) and schedule other activities so that they do not conflict with the examination dates.
Success and Studying
Success and Studying for the class:
This is an online course. To be successful, check the course daily, read announcements, including those on Discussions, read and respond to course email messages as needed, complete assignments by the due dates specified and if at all possible well ahead of the due date, communicate regularly with your instructor and peers on Discussions and make sure to remain aware of the assignment schedule to stay on track.
DO NOT MAKE INFERENCES ABOUT DUE DATES AND TIMES. If exams follow some discernible day of the week pattern, for example, that doesn't mean that the final exam will follow the same pattern. Do not make guesses when assignments and exams are due.
To master the concepts, complete all homework assignments and review/study the powerpoints and the textbook thoroughly. It is important that you practice active engagement. What this means is explained below in the subsection "Does course content need to be memorized?"
Study Advice:
It might be helpful to create your own lists (or perhaps 3x5 cards) of definitions, procedures and theorems. Writing helps to build active knowledge.
You must learn and study continuously throughout the duration of the class. Relying on “just in time” cramming for exams is an ineffective study technique and will virtually guarantee failure in the class.
Some of the exams ask you to write proofs. Proof writing skill is like learning a language. To learn a language, you need to practice speaking it. Passively reading or listening to it will not suffice. Likewise, the ability to write proofs can only be gained by writing proofs, not by merely reading proofs other people wrote. It is imperative that you practice writing proofs in preparation for being tested on your proof writing skill. It is unlikely that you will write a correct proof on an exam if it is your first attempt at writing a proof.
Do not abuse help. Math learning happens when you struggle with a problem. If you ask a tutor or on Discussions how to get a problem started at the slightest sign of difficulty, you will not get as much learning out of the problem as you would have if you had spent some time first thinking about the problem and trying to connect it to the material covered in the lectures.
Don't go shopping for answers. Some of the material in the class is abstract, and abstract ideas require an investment of mental effort of your own to understand them. If you do not understand a concept, do not immediately jump to the conclusion that it must be the lecture's fault for not being clearer, and go looking on the internet for a better video or ask the teacher for more resources. Videos cannot do your thinking for you. Don't confuse information gathering with studying, and don't mistake superficial how-to knowledge you may gain from Khan Academy videos for conceptual understanding. Time searching for third party videos is better spent working with the information you got and asking for clarification on Discussions.
Review the theory connected to the problem carefully. What concept am I not understanding correctly? When you struggle with a problem like this for some time, and then have an aha experience, that's when mathematical learning happens.
Create your own examples to clarify and illustrate the theory. Mathematical learning requires active engagement with the material. No amount of passive consumption is a substitute for that. You have to be a doer, not a consumer.
Mathematical Reasoning
Mathematical reasoning is one of the official learning goals in the course description of the class.
Perhaps high school got you used to thinking that "doing math" is just mindless imitation, following cookbook recipes and plugging numbers into formulas. It isn't. Real math is about coming up with the formulas in the first place and being able to justify them. It's about critical thinking, about seeing common patterns, about understanding how procedures we learn depend on assumptions and agreements we made in the first place ("definitions"), questioning whether or verifying that, or judging to what degree, the agreements are appropriate to the situation at hand, and being aware of how different assumptions lead to different "right" answers. It's about independent application of a theory you have learned to practical situations where the connection may not be obvious. It's about ability to modify the theory if an application demands it.
This is ultimately about teaching you employable skills. If Wolfram Alpha can do it, no one will pay you to do it. Mindless application of procedures is for computers. They're way better at that than you will ever be.
What this means for this course is that some homework questions are intentionally designed to not be solvable by mindless imitation, by just looking up a similar example in the videos and substituting new numbers. It is not an oversight of the teacher or bad course design that there is no practically identical problem in the videos or the textbook that would allow you to solve your homework problem by just changing numbers. It is an intentional difficulty, built in to stimulate your mathematical reasoning ability and your understanding of the underlying theory.
You should feel free to ask questions about such problems, like all homework problems, on Discussions, but you should expect the teacher to give you only hints to stimulate your own thinking process. Do not expect to receive a fully worked solution to a slightly similar problem. The learning goal is not to blindly follow a recipe, it's to get you to apply what you have learned independently to a new situation. It wouldn't be a new situation, or independent application, if you have an example problem with a model solution to imitate.
Learning Mathematical Reasoning
Mathematical reasoning can only be learned through persistent practice. Homework is where much of this practice happens. The lecture material is designed to help you develop conceptual understanding, not necessarily walk you step by step through every homework problem. If you find yourself challenged by a homework problem, and cannot find a fully worked model problem in the course videos that looks the same, that does not mean that the material was not covered in the lecture. The theory necessary to solve the problem was covered, and now it is your job to determine how the theory applies to the homework problem. When you connect some of the dots yourself, that's when mathematical learning happens.
Struggling with a problem, perhaps for an extended period of time, is an expected and normal part of this process of developing mathematical reasoning skill, not a breakdown of your educational experience. Persistence in this struggle usually pays off, and results in deeper conceptual understanding. If you give up after a solution has not presented itself after a short time, and find a tutor or third party video that walks you through this exact type of problem, you are depriving yourself of the intended learning experience.
Learning mathematical reasoning is a lot like building strength or cardiovascular fitness - it happens slowly and somewhat painfully, through regular exercise, and cannot be cheated. If there is no pain, then there is no gain. Services like Chegg and, to a lesser degree, Khan Academy, are the personal trainers who lift the weights for you as you watch, or the golf cart service that drives you around the running track. You will take away a certain familiarity with the "gym" or the scenery of the "running track" that can be mistaken for learning, but the exams will dispel that illusion.
If you found a third party video that made it much easier to complete a homework assignment, ask yourself honestly whether you actually ran the distance, or were being chauffeured to the destination. If you never broke a sweat, it's probably the second.
A habit of taking shortcuts on the homework will come back to haunt you on the tests, in future classes and in your professional career. It is not turning in the right answers that will prepare you for the future. It is having found the right answers on your own.
Does course content need to be memorized?
The question sometimes comes up whether parts of the content, such as the logical equivalence rules of chapter 1, the common summation formulas of chapter 2, or the big-O relationships of chapter 3 need to be memorized. The question is not easily answered because it is based on the false premise that those particular bits of knowledge can only be acquired through (blind) memorization. The best answer is, students are expected to acquire a detailed familiarity with the course content, but not through memorization.
Certain types of knowledge, such as dates of historical events or the sizes of planets, are basically "random" and can only be learned through memorization. Mathematical knowledge, on the other hand, is not "random" but interconnected. All facts except the so-called axioms follow logically from other, simpler facts. Mathematical knowledge rests not on memorization, but on an understanding of this web of logical relationships. It is naturally acquired through (usually several iterations of) theoretical study and practical application.
For example, there is no need to memorize that "given that p implies q and given q, p must be true" is a fallacy. This follows directly from the fact that a conditional and its converse are not logically equivalent.
If you find yourself wondering whether this or that bit of course content needs to be memorized, then you are not studying correctly. Ask yourself why the formula or relationship is true, or what motivated the definition. Can you prove it? Create some examples of your own to test the formula, or to illustrate the relationship or definition. Think about how the fact in question is relevant to applications. If you are a CSE major, ask yourself how you might encounter this issue in a programming or software design context. Consider how the formula, relationship or definition could be generalized.
This is what is meant by "actively engaging with" the content. Once you are done with that, you will find that you have not only naturally committed the fact to memory, but you have done so in a way that is superior to mere memorization. Trivia that are merely memorized are easily forgotten again, having made no lasting impression on your mental environment. Ideas that you have thought through, on the other hand, will be yours for a lifetime.
Some words on learning styles
Despite the persistent popularity of learning style theories among students and educators, research has shown that learning styles in the sense commonly believed - hardwired limitations on the ways in which we can effectively receive and retain knowledge - do not exist, only learning preferences. You may like to receive information visually, but that does not make you a "visual learner" in the sense that your brain is fundamentally unable to process, say, verbal information; nor does it mean that you will retain information better if it is presented to you visually.
Research has failed to produce evidence that customizing teaching towards individual learning preferences improves learning outcomes. There are well-founded concerns among some psychologists and researchers that the practice of identifying and labeling students according to learning style models imposes limitations on students' abilities and is actually harmful for learning.
This is likely the case in higher math, such as it is taught in MAT 243. Mathematical understanding benefits from synergy, from holistic understanding that engages all our senses and mental abilities and includes verbal/intuitive, verbal/conceptual, symbolic/algebraic, numeric, visual/geometric, and physical. We all have these abilities, though there is individual variation in how strong they are. Do not sell yourself short by denying yourself the full range of your abilities and believing that all but one are beyond you.
Regardless of your own learning preferences, try to develop your own mental images, evocative verbal descriptions and memorable physical metaphors for abstract concepts. This is what most people in STEM do.
Calculus provides some good examples for how a mathematical concept can be understood in different ways and appeal to different kinds of thinking. Consider the derivative of a function f.
Symbolically / algebraically, f'(x) is defined as the limit of (f(x+h)-f(x))/h as h goes to 0.
Numerically, you can understand this by making a table of values of the quotients (f(x+h)-f(x))/h for smaller and smaller h values.
A visual/geometric interpretation of f'(x) is the tangent slope of f at the location x.
A physical interpretation is obtained if you think of x as time and f(x) as position of a moving object. Then, f'(x) is instantaneous velocity at time x. The phrase evokes a mental image of movement and change.
A verbal/conceptual interpretation is that f'(x) is the instantaneous rate of change of f at x, which lends itself to verbal/intuitive conceptualizations of f'(x) being a measure of how quickly a function's value is changing at or very near a point.
Some have suggested calling the derivative of f the sensitivity of f instead. It is unfortunate that that is not the official name, because unlike the fairly meaningless word derivative, the word sensitivity describes what it is that f'(x) actually measures: how sensitively the function's output reacts to changes in input at a point x. f'(x) = 3 means if you change the x value a little, the y value will also change, but by about 3 times as much as the x value.
Discrete Math learning similarly benefits from good mental images, verbal descriptions and physical metaphors. Take for example the concept of the conditional. Conditional relationships can be phrased in many different ways, some of which are covered in the lecture: if .. then, .. only if .. , and using the words "necessary", "sufficient" and "unless". Those are the standard verbal metaphors for conditional relationships. In addition, we can create our own illustrations and analogies.
As suggested in the lecture, you can think of the conditional as a promise. This analogy makes it clear why the conditional is automatically true if the premise is false- it's because the condition upon which the promise was based was never met in the first place.
You can come up with any number of mechanical cause and effect relationships that illustrate p → q:
p represents whether the heating is turned on in a home, and q represents whether it is warm in the home. Then p → q is always true: when the heat is on, it will be warm. When the heat is off, it could still be warm (for example, due to outside heat), but it can also be cold. p → q simply doesn't give us any information about q in the case that p is false.
p represents whether the sun is shining, and q represents whether it is day time. Then p → q holds: when the sun shines, it must be day time, and when the sun doesn't shine, it could be a cloudy day, or night. So a true p forces a true q; a false p doesn't give any information about q, and permits either truth value of q.
The point here is not to provide additional lecture material, but rather to illustrate what active engagement means in practice and to encourage you to create your own metaphors, examples, analogies and applications of the material.
Back to the topic of learning styles, if you have a strong preference for one type of learning, then focus in your active engagement with the material on translating the content into your preferred way of processing and memorizing information. The key is to not wait for the teacher to do this translation for you, or to seek out third party resources that do it for you, but to do it yourself. It's only when you do this mental processing yourself that you create the conditions for deeper understanding.
Homework and Discussions
Murphy’s Law of online homework systems: something always happens on the evening of the due date. You should work on homework assignments continuously and finish well before the due date. Failing to do this will not entitle you to a time extension in case of a server breakdown, broken computer or personal emergency. The same applies for the period during which you can earn extra credit for early completion.
If you need help with the homework, don't email the teacher. Ask on Discussions. Below, you will find guidelines on how to ask questions on Discussions.
Edfinity questions are set to allow only a limited number of attempts. This is intentional, to discourage trial and error solutions, or worse, a purely combinatorial approach wherein you go through all combinations of answers on a multiple choice question until you find the right one, thereby reducing the homework to a guessing game. If you are not certain what the answer is and you are on your last attempt, seek help on Discussions.
Discussions: It's not a bug, it's a feature.
Do not think of being challenged by homework questions and needing help as a breakdown of your educational experience in this class, and Discussions as a kind of tech support that must fix this breakdown for you asap by essentially telling you the answer.
When you ask a question about a challenging problem on Discussions, which leads to a discussion that makes you verbalize your thinking and ends with you having that aha experience of what you were missing - that's not the system breaking down, or the teacher's plan failing you. The discussion is not the teacher doing emergency repair work that should never have been necessary with a better course design. It's the system and the assignments working as intended. This is when math learning happens. It's the Socratic method.
This system requires your active participation and initiative. The more you put in, the more you receive.
You are expected to read what has already been discussed on Discussions about a problem before posting your own questions. Do not post questions that have been asked and answered already. If you make posts that indicate that you did not read what has already been said, the teacher may refer you to existing posts. Not having to sift through a lot of discussion that has already occurred is one of the benefits and privileges of starting your written homework and asking your questions early.
Ask for help by asking a specific question and explaining your thought process so far. Give your "best" wrong answer if possible. You have to give the rest of the class and the teacher something to work with. Merely saying "I don't understand how to do this" or "Edfinity doesn't accept my answer" will usually just provoke follow-up questions and waste time, rather than result in usable answers.
Airing generic grievances about not understanding whole concepts or sections, along the lines of "I spent hours trying to figure out the growth of functions, it makes no sense to me" is even less helpful. The teacher and classmates won't even know where to begin if you write that. It may very well be the case that you don't understand a whole set of ideas, but it is your job to identify a starting point. Identify the first thing you don't understand, and then ask specifically about that.
Help us (us meaning the teacher and the other students) help you by giving us something to work with - include what you DO know or think you know already, not just what you don't know.
For example, instead of asking "I just don't understand codomain", you might ask "I thought what you explained as the codomain was the range. Can you give me another example to clarify the difference?"
Or, instead of saying "The floor function makes no sense to me!" you might say "I don't understand how the floor function acts on negative numbers. I feel that the floor of -2.5 should be -2, but it is -3. Can you explain this again or in a different way?"
FAQ
Some of the Quizzes are too hard! I'm fearing for my grade.
Some of them are indeed intentionally challenging. They are designed to give you an honest assessment of your understanding of the concepts and your ability to use them independently in applications. They are to guide you to what needs to be studied and reviewed in more depth.
There is no reason to panic over bad quiz grades. The quizzes are collectively worth only 5% of your grade.
When should I take the quizzes?
At the very least, you should have studied the corresponding lecture material thoroughly first. It is also good to work some of the Edfinity problems first, because they give you multiple or even unlimited retries. Remember, the quizzes are mainly meant to be diagnostic, so you should not take them too early in your study process.
The written homework is too hard. I have to figure out too much on my own. I don't get the information I need from lecture and examples.
It is true that some of the written homework problems are more challenging than the kind of mostly mechanical homework problems you get in college algebra or calculus. That is because they are meant to provide an opportunity to learn mathematical reasoning, which is one of the learning goals of MAT 243 (it's in the official course description). Mathematical reasoning can only be learned by doing the reasoning. The information you need is all there in the lectures, but it's your job to connect the dots and see how the information applies to the homework problem. A homework problem that is identical to a lecture example except for a few minor changes does not challenge you to practice your reasoning skills.
Again, there is no reason to panic over this. Written homework is only worth 3% of your total grade.
Why are the extra pages in the expanded powerpoints not in the filmed lecture videos?
They were added after the lecture videos were filmed in response to difficulties some students experienced with the homework. By and large, the content of the extra pages is not lecture material, i.e. not basic theory, but rather, understandings and connections you can and are expected to make on your own while you watch the filmed material and work through the written homework assignments. The pages exist as a safety net, in case you didn't make those connections on your own.
Do not think of the additional pages as extra lecture material you have to learn without the benefit of videos. Think of them as your questions anticipated and already answered in detail.
Having videos and then expanded powerpoints is really no different than having an in-person lecture plus a textbook. The textbook does not contradict what is said in the lecture. It just expands on it, goes into more detail, covers additional questions, etc.
Can you recommend additional resources?
This question is sometimes asked by students who are not using the resources they already have effectively: the textbook, the course videos, powerpoints, extra examples (videos and powerpoints) and Discussions. If some topic does not make sense to you, even though you read the corresponding section in the textbook, watched the course video, reviewed the powerpoint and looked at the extra examples, it is unlikely that a different textbook, another video, etc. will make a difference.
It is better in this situation to ask questions on Discussions.
The teachers are aware that the specific additional resource that students who ask this question often have in mind is a fully worked out model problem that is identical to a challenging homework problem, except that a few numbers have been changed. Many homework assignments are indeed of this type, but not all. This is intentional, as routine problems that come down to symbol substitution cannot develop mathematical reasoning skill.
If there is no model problem, ask for help on discussions and do not take an initial hint posted by the teacher as the last word, but rather, as the first post in a conversation. It's up to you to keep this conversation going.
Generally speaking, making generic requests for "additional resources" about a whole topic will be unproductive. There are no secret additional videos that the teacher is withholding. The discussion forum and the teacher's knowledge of the subject are the additional resources. Skip the meta-request for additional resources and ask for help on the specific idea you are not understanding. For example, instead of asking "I don't understand summation. Can you recommend additional resources?", ask "I don't understand how the summation formula on page X on the lecture Sequences and Summation is simplified."
Why are quizzes, written homework and Edfinity worth so little? I feel like I'm working for nothing.
Giving most course credit for proctored assessments is the only way to protect the integrity of the course. That does not mean though that your work on the unproctored assessment is for nothing.
Homework (quizzes, written homework and Edfinity) is where most of your learning will happen. Completing homework conscientiously and with a mindset of active engagement is what enables you to pass the exams. The inverse of that is usually also true: not doing homework leads to failing grades on the exams.
On the homework, you earn the currency of mastery of the material. The exams are just a device for exchanging that currency into course credit. Course credit earned on exams thus also rewards you for your homework.
Can't the graders leave more detailed feedback for written homework?
It would indeed be desirable if graders could leave extremely detailed feedback and basically comment on every sentence or equation you wrote. Unfortunately, this is not possible because graders are not paid for the number of hours that would be required.
Why am not receiving any feedback on written homework?
Graders are instructed to leave feedback when they take away points. Canvas supports two types of feedback: (1) comments left in a text box, and (2) annotations put directly into the pdf file. Graders are encouraged to use the second type, because it supports highlighting to show where exactly a mistake occurred.
Annotations are not shown in your Grades page. The little comment symbol next to the assignment will only show you (1). You need to click on the homework and then click on "view feedback" to see (2).
Is Discussion Participation Required?
It is not required, but expected. If you earn failing grades on assignments, and do not participate in discussions, your non-participation in discussions may be mentioned in an academic warning. Failure to participate in discussions has no direct consequence on your final grade, but it may have a large indirect, cumulative impact on all your grade components, in the form of you not benefiting from the learning opportunities that discussions offer.
If you are a very strong student, consider that by explaining problems to others, you will practice the important ability to communicate mathematical ideas. This skill is valuable not just for those who wish to go into teaching, but for all STEM workers, including those working in corporate environments.
How are multiple answer questions scored on Canvas exams or quizzes?
To calculate scores for Multiple Answers quiz questions, Canvas divides the total points possible by the amount of correct answers for that question. This amount is awarded for every correct answer selected and deducted for every incorrect answer selected.
I don't understand how extra credit on the exams works. I just took test 1 and got 84 points. What is my grade on test 1?
The instructor will post test grades that take extra credit into account after the testing period is over.
On test 1, there are 92 points and 8 extra credit points. 84 points is a grade of 84/92, or about 89%.
Why has my academic status report not been updated?
Academic status reports are not live tallies of your class performance and can't be updated. They are snapshots of your class performance on the specific date they were issued and will continue to show only what your performance was as of that specific date. The teacher may or may not issue new status reports. You can always see in your Canvas grade center what grades you have earned so far.
What is my current grade in the class?
The concept of a current grade in the class while grade components are missing is not as straightforward as you may think. The weights in this syllabus define a final grade, but they do not define partial grades.
Say you just took test 1 and want to know your current grade. You got a grade on quizzes and homework taken so far. All quizzes and homework are worth 10% of your final grade. Test 1 is worth 20%. Thus, less than 30% of your final grade components are represented, or exactly 30% if we assume that your quizzes/homework so far are representative for all the missing ones. We could now take the weighted average with a total weight of 30%:
The problem with that is that it gives undue weight to the quiz/homework component. In this calculation, the quiz/homework component accounts for 1/3 of your total, even though it will only be worth 10% of your final grade.
To fix the relative weights, we could just weigh Test 1 at 90%, which is equivalent to the not totally unreasonable assumption that your test 1 grade is how you will perform on average on all exams. Then
This estimate is more plausible, but it's still an attempt to calculate something that is intrinsically unknowable because sufficient data does not exist to compute it. Some students do badly on a first test and then improve dramatically on subsequent tests. For others, it's the opposite: a great first test followed by worse and worse performance on subsequent ones. Yet other students perform consistently.
No math can predict which of these types - if any - you will be.
There is a third way of computing your "current" grade: just assign zeros to all assignments/test grades that you have not yet turned in/have yet to receive. This concept of current grade would assign failing grades to almost all students until the final exam has been written. You may think this is unreasonable, but it is meaningful in a way. It represents the grade you would receive for the class if you stopped working altogether at this point.
You can see the fundamental problem with the concept of a current grade: it depends on arbitrary assumptions about future events that are unknowable. So it's really pseudoscience. It's somewhat like poll numbers for an election that is still months away.
Instead of asking for a questionable number, make some reasonable inferences yourself. Are your exam grades all well above 60%? Then you are likely to pass the class if you maintain your current work habits. Are your exam grades consistently much below 60%? Then you are at high risk of failing the class, and almost certain to fail if you maintain your present level of commitment.
If you insist on wanting a numerical prediction of your final grade, just take your exam average. Given that exams account for 90% of the final grade, this is a somewhat plausible estimate, especially if you have been doing your homework decently so it neither adds nor subtracts much from your final grade.
Have you not been doing your homework at all? That will cost you a letter grade in the final grade calculation.
Use your own common sense, and don't fall for the tempting fallacy of "current grades" that come with a magical air of predictive power by being computed to 2 decimal places.
I worked with a math tutor but even the tutor could not help me. Can you help me with these problems?
Solid conceptual understanding of discrete math topics is not as common among math tutors as are procedural skills in college algebra and calculus. Working with a tutor whose knowledge of discrete math is weak, not receiving good help and then asking for Discussions help after all is not as good a use of your time as asking on Discussions in the first place.
Ask questions on Discussions, and be prepared to engage in a conversation. You may not just be told what the answer is, the way a tutor might. The teacher may respond to your question with more questions rather than answers. This can be frustrating, but if you give the process a chance, it is likely to result in you having a genuine aha-moment and understanding a concept that was previously eluding you. Being told what the answer is will not result in the same learning experience.
