Discrete math study strategy - Tips and advice

[eseefreak]

Hi everyone,
I haven't been successful in Discrete Math this semester. I have finished all of the calculus I-III series and I did very well. I want to know if anyone can give me some tips on how to study for my final coming up in a few days.

Now, I understand that is a vague question but I am looking for advice as to how I should approach problems in Discrete Math. How long I should take to overview, and re-learn some concepts? What worked for you?

I have found that Discrete Math contains a wide variety of concepts, theories, and proofs. I have 3 days to overview/study everything, and I am pretty familiar with everything we went over this semester but I am no where near ready for my final.

Any additional advice as to how they were successful in studying in this course would greatly be appreciated.

Thank you! :)

 

[Stephen Tashi]

If it's not an open book test, make sure you've memorized relevant definitions - if possible, in the original wording , not "in your own words".

"Discrete math" can mean a variety of different courses. If you want specific advice, you should outline the topics that were covered.

 

[eseefreak]

If it's not an open book test, make sure you've memorized relevant definitions - if possible, in the original wording , not "in your own words".

"Discrete math" can mean a variety of different courses. If you want specific advice, you should outline the topics that were covered.

We are allowed a page of notes, so that can help during the exam.
We covered:
Truth tables
Negations
Existential and Universal Statements
Proof of an existential statement
Direct proof of a universal statement
Disproof of a universal statement
Indirect proof of a universal statement
Sequences, summation/product notation
Mathematical induction
Set theory
Functions
Relations
Counting and Probability: counting elements in a list, possibility trees, multiplication rule, permutations, the addition rule, complement, inclusion exclusion, combinations, permutations with repeated elements, conditional probability/Bayes thm., independent events, expected value of a random process with numerical outcomes.

So we covered a lot of topics and really got into the details for each of them. Good tip, I shall write my notes as listed in the original text-it will make things less confusing.

Could you think of any other tips regarding the subjects I covered? Note taking, studying, or whatever comes to mind?

Thank you! :)

 

[Stephen Tashi]

The way my mind organizes your topics is:

1. Logic:
Truth tables
Negations
Existential and Universal Statements
Proof of an existential statement
Direct proof of a universal statement
Disproof of a universal statement
Indirect proof of a universal statement

2. Index notation and manipulation:
Sequences, summation/product notation
Mathematical induction

3. Basic mathematical structures
Set theory
Functions
Relations

4. Combinatorics
Counting and Probability: counting elements in a list, possibility trees, multiplication rule, permutations, the addition rule, complement, inclusion exclusion, combinations, permutations with repeated elements

5. Probability
conditional probability/Bayes thm., independent events,

6. Random variables
expected value of a random process with numerical outcomes.

If I were making up a work-the-exercise test, I'd give about the same number of questions on each of those 6 major divisions. (By contrast, on a multiple choice test, you might get a question on each of the individual topics you listed.)

My advice is "Breadth before Depth"; begin by picking a few "medium difficulty" homework problems from each major division and review them. Don't pick problems that were extremely hard. Don't pick problems you found trivial. If you have time left after doing that, study a few of the harder homework problems.

Mathematics teachers hope to build up later topics using earlier topics. If that is successful, they can test on the later topics and this is also a test of whether you know the earlier topics.

My personal design for a short final:

1. A problem about truth tables

2. A problem involving both negation and quantifiers - for example, a problem invovling negating a statement that has both a "for each" and a "there exists" quantifier. - or perhaps the task to disprove a statement involving quantifiers because you'd have to understand the negation of the statement in order to prove it.
.
3. A problem about mathematical induction (This topic is so important, you're bound to get such a problem)

4. A fairly simple problem on Basic Mathematical Structures just to test whether people can interpret the definition - something like "is the set ... a function ?"

5. A question about sets that is "a direct proof of a universal statement" - for example, prove (A intersection B) is a subset of A.

7. A problem on Combinatorics. ( I don't find such problems easy or interesting, so I'd only give one. If you detect your teacher has an enthusiasm for combinatorics, you can expect more than one.)

8. A problem on probability. If your teacher enjoys combinatorics, you might get a problem involving it - problems about drawing certain cards from deck, problems about throwing several dice etc. I prefer the kind of problem where you are given the probability of certain events A,B,.., C union D, etc. and asked to find the probability of some other event like "B intersection D complement"

9. A problem to find the expectation of a random variable. There are many topics associated with Random Variables but if your class only covered finding the expectation, that limits the questions on it.

I'd be interested if my design resembles what you get.

 

[eseefreak]

The way my mind organizes your topics is:

1. Logic:
Truth tables
Negations
Existential and Universal Statements
Proof of an existential statement
Direct proof of a universal statement
Disproof of a universal statement
Indirect proof of a universal statement

2. Index notation and manipulation:
Sequences, summation/product notation
Mathematical induction

3. Basic mathematical structures
Set theory
Functions
Relations

4. Combinatorics
Counting and Probability: counting elements in a list, possibility trees, multiplication rule, permutations, the addition rule, complement, inclusion exclusion, combinations, permutations with repeated elements

5. Probability
conditional probability/Bayes thm., independent events,

6. Random variables
expected value of a random process with numerical outcomes.

If I were making up a work-the-exercise test, I'd give about the same number of questions on each of those 6 major divisions. (By contrast, on a multiple choice test, you might get a question on each of the individual topics you listed.)

My advice is "Breadth before Depth"; begin by picking a few "medium difficulty" homework problems from each major division and review them. Don't pick problems that were extremely hard. Don't pick problems you found trivial. If you have time left after doing that, study a few of the harder homework problems.

Mathematics teachers hope to build up later topics using earlier topics. If that is successful, they can test on the later topics and this is also a test of whether you know the earlier topics.

My personal design for a short final:

1. A problem about truth tables

2. A problem involving both negation and quantifiers - for example, a problem invovling negating a statement that has both a "for each" and a "there exists" quantifier. - or perhaps the task to disprove a statement involving quantifiers because you'd have to understand the negation of the statement in order to prove it.
.
3. A problem about mathematical induction (This topic is so important, you're bound to get such a problem)

4. A fairly simple problem on Basic Mathematical Structures just to test whether people can interpret the definition - something like "is the set ... a function ?"

5. A question about sets that is "a direct proof of a universal statement" - for example, prove (A intersection B) is a subset of A.

7. A problem on Combinatorics. ( I don't find such problems easy or interesting, so I'd only give one. If you detect your teacher has an enthusiasm for combinatorics, you can expect more than one.)

8. A problem on probability. If your teacher enjoys combinatorics, you might get a problem involving it - problems about drawing certain cards from deck, problems about throwing several dice etc. I prefer the kind of problem where you are given the probability of certain events A,B,.., C union D, etc. and asked to find the probability of some other event like "B intersection D complement"

9. A problem to find the expectation of a random variable. There are many topics associated with Random Variables but if your class only covered finding the expectation, that limits the questions on it.

I'd be interested if my design resembles what you get.

I really like your short final outline design. It helps organize the chaos that is scrambling in my brain. I had no idea these topics were grouped this way. I will definitely tell you if your design resembles my final examination. Thank you for taking the time to help me with a general outline. I have a lot of work to do :)