**Assignment (due Thursday, December 13).** Imagine that you are invited to speak on the first day of MAT 2071, to give advice to entering students. Write *at least three sentences *responding to *at least o**ne* of the following, describing what you would tell them.

- What do you wish that you had been told at the start of this class, to help you succeed?
- Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.
- What is the most important
*prior knowledge*(not taught in the class) that you need in order to succeed? Why is it important?

**Extra Credit.** Respond to someone else’s comment. Do you agree? disagree? Have anything to add?

2.Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.

The topic I had and still have most difficult is the topics involving sets and its proofs. This topic of sets sneaks in throughout the course and not understanding the meaning of it can affect your methods of attacking the problems. To master it I recommend asking questions when you don’t fully understand what’s being written in the board, while this subject is being taught. Do the homework will help a lot but do not attempt the homework last minute. The most important thing to remember is the basic notation and how writing it affects your proofs. with that being said Good luck!!!

Dear Junior,

Yes, I totally agree with you, especially about the homework part. Because doing homework gives a chance to practice, practice, practice and review class material.

2.Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.

3.What is the most important prior knowledge (not taught in the class) that you need in order to succeed? Why is it important?

I found induction proof is one of the most challenge methods that we learned in class for proving . It’s used to prove universal statements about natural numbers. In other word, it can be used to prove something that is true for every natural number. There are two steps we need follow. First, the base step, we need to show the statement is true for the first case. Second, the inductive step, we need to show the statement is true for k+1 case if the k case is true. In order to master this topic, I would suggest you start from the beginning and the end. Try to write down what is given (the beginning) and what we need to reach (the end). Then try to make connection with them to figure out the middle part. I feel the algebra knowledge is important in this topic. Because you need to be able to observe, simplify, and manipulate by using algebraic skill in order to complete the middle part.

I totally agree that proof by induction was one of the most difficult things we learned. Direct proof and contrapositive proofs were pretty fun and relatively simple, but proof by induction required a lot more time and thought!

“Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.”

I think the hardest topic is the proof part. It is hard because you have to understand the question first and decide which proof to choose to prove your answer. You can easily figure out the starting and ending points, but it is hard to fill up the middle part. Then, you ask yourself: What I should write? How am I going to prove this statement? You have to memorize every definition you learned in class, and since everything you learn in class is connected, you will use a lot of information when you try to prove the statement. In the beginning, when you start learning about sets, cardinality, etc., you might think it is easy, but don’t become too confident about it. This class is like building a new building, and that’s why the foundation is essential. If you don’t want it to collapse, then come to every class and try to take notes, which will help you clarify your thoughts and encourage deeper thinking about the topic. Another piece of advice is to do your homework on time. If you don’t understand something, don’t wait until the last minute to ask. The professor will always help you, and you can email him anytime. This class is like a puzzle. If you come to every class, you will receive new information (puzzle pieces) to finish your puzzle. Then, you will complete your puzzle successfully. Get ready to acquire new information to improve your knowledge.

2. Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.

The one topic of the course that is challenging for me is proofs. Proving the proofs during class and for homework, I understand everything of what I’m doing and what steps I need to do to prove or disprove the proof. For the exam I feel like you have to make sure you study enough to where everything flow while your solving the proofs. I get stuck, and being timed is just makes me stressed out that I can’t think things through. Having to remember the definition of things also was challenging. The advice I would give to master proofs is to always asks questions, never leave class not understanding the work. Also ask questions about the homework. Doing the homework with out looking at the answers in the back of the book helps you understand the proofs better also. Study hard, work harder and you will do well in the class.

I think that the most important prior knowledge one needs to succeed in this course is knowing how to manipulate equations. Proofs are probably the toughest part of this class, but they’re much easier if you know how to manipulate an equation to fit the needs of the proof. If you can see an equation in more than one form then proofs really are not so difficult, since the questions often require you to pull out common factors or split up like terms. Proofs are actually pretty fun in my opinion for this very reason.

I agree with you Rachel, as long as you know how to manipulate an equation for the proof problem it makes it easier to solve the proofs . I do feel like the proofs are actually fun.

I agree this is a key thing to know by manipulating equations. Often times I had a hard time with problems due to this

My advice would be to always keep track of your work and try to avoid doing everything las minute. You must do all your homework. This will also prepare you for exams. There is much extra credit you can earn. Do all of them if possible to get maximum points. Be sure to ask questions if you do not understand something, to avoid falling behind. Professor Reitz is always happy to explain it again. Keep track of you work. I wish I knew to start studying in advance. I would usually study after I would see the review sheet. However, you have accesses to last year’s review sheets, so you can take advantage of that. Overall, if you keep track of all your work, and take advantage of all the ext4ra credit, you should enjoy this class!

Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.

I’d say induction was most challenging. It seemed easier than it actually was. A tip I would give is to practice with class mates to get others perspective. Sometimes that’s enough to understand

1. What do you wish that you had been told at the start of this class, to help you succeed?

When the semester first began it seemed pretty easy. We were told to read “ The advice for the future” written by the previous class as you are doing now. Majority of the advice given was great information. Some advice I will reiterate:

1. Do all your homework , The practice helps and every bit of the points count. Submit written work even if your late. Remember WeBWorK cannot be submitted late.

2. Study the terms.. This is Crucial. Everday you come in you receive a new set of definitition/ theroems. By the final you will need to understand each one in its entirety.

I can’t say there was anything that I wasn’t told, What I would say is take all the advice serious. The beginning of the class will seem like a walk in the park. BUT TRUST ME …. IT gets complicated.

Your exams do not define your overall grade so do not get discouraged. Still aim for a perfect grade but as long as you do EVERYTHING else you will do good.

2. Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.

Proofs can be Misunderstood. I still can’t wrap my mind around the whole concept to explain it. But when you get it you will be so proud of yourself ( at least I was). The goal is to to prove propositions and conjectures with general rules, facts and principles. The generality of it can be confusing but Professor Reitz is great at explaining it as best he can. Ask questions if you don’t understand he will reword and give examples it as much as he can for you to get it. If you still don’t get it he’s willing for a one on ones during his office hours.

GOOD LUCK!!!!

2.Choose one topic in the course that is especially challenging. Identify it and give advice to students trying to master that topic.

The topic which was difficult for me to understand was the proof topic. We were asked to proof a proposition by using either direct proof or contraposition proof or contradiction proof. The challenge was how to start the proposition and how the proposition will end. The only way I can understand the topic is I began to walk through the example that professor Reitz gave in class and started to do three proof problems every day to master the proof cases. My advice to the new students is to work hard on the proof cases and ask questions if you don’t understand the process or procedures to proof proportion. Also, there is no escape from proof topics. 70% of the class is proofing proportion. Good luck in the class.