**Assignment (due Thursday, December 17 – final exam day).** 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?

Thankfully, through the assignment of reading the advice from the past in the beginning of the semester, I read the advice of completing all the homework in order to get more practice of the material presented in the class. The topic that was challenging for me was relations. I had a great confusion determining the difference between the different types of properties. Many seem to be related to each other, if not, appearing to mean the same or opposite as others. I hope you guys get a better understanding on this topic than I did but confusions can be clarified by simply asking Prof. Reitz who is always happy to help :D. If you have taken trigonometry in high school, this class will refresh your memory on several concepts covered such as probability, the binomial theorem, and other topics that cant come to mind at the moment lol. Over all this is a fun class and you learn at the same time. I hope you guys like puzzles because you will find a couple in this class. Have fun guys.

I agree with you Irania, it been fun class, and the group project was great. Yes, do your homework and practices with the proofs because when go into contradiction, you will have trouble understanding idea of it. If you must always bug Proffessor Reitz, the homework get more challenging as you progress into the class.

To the new students that taking Proof & Logic, do your homework because it will help you during the exams, and if you have questions ask Proffessor Reitz. Do not hesitate to ask questions because this class may look simple, but it will be hard if you lack practice. The only prior knowledge you may need is basically idea of union in Probability & Statistics, what is Fibonacci sequences, and basically knowledge of vocabulary in mathematics that you may studied in k-12, but never gone over actually meaning to it.

One piece of advice about Proffessor Reitz, he will sometimes take leave for a whole week in the semester, when that happens or not make sure it not during the month of finals especially the week before finals because that happened to our class. You will suffer for going whole week before finals without any proofs.

The topic that twisted my brain the most was proof by contradiction. What confused me, was that you trying proof if was it opposite, so if it was true, you will proof it false. Then if there something wrong with the proof, it will become true, thus you proofed the statement. My advises ask questions and do homework because when get up to proofs, the detail really matters in proofing something, and Euclid Lemma.

Agreed. The leave, one week before finals, really puts us in a tough spot. It was actually amazing to realize that I was practically begging for Proofs. Well, that just cements the idea that we should practice everyday or else we will be behind because of unfavorable circumstances. Practice. Practice. Practice.

I forgot to mention, Proffessor Reitz is good professor, you will enjoy taking the class, and do the homework.

Proof. Proofs. Proofs. The course name is Proofs and Logic so it shouldn’t be a surprise that both of those would be an integral part of the course. It begins with simple logic like truth tables and statements. Nothing too hard as the topics discussed is nothing too ground breaking considering prior knowledge of algebra. However, your ability to logically reason and explain yourself is tested when it comes time for proofs.

Do not falter. The difficulty spikes when it comes time for proofs, like induction. However, simply giving up is not an option. I believe that with increased difficulty comes an increased feeling of accomplishment. Don’t worry. There is always an answer to Dr. Reitz’s problems. If there is no answer, he has pulled a fast one on you and the answer is that there is no answer. Haha. That’s just part of the fun.

Practice. Homework and classwork is assigned for practice and to show that you can implement what you’ve learned. Dr.Reitz is available in and out of class to answer questions and help out. Going through the semester without talking to him at least once is like shooting yourself in the foot. Proofs require a certain amount of imagination to be able to decipher the reasoning behind statements. With enough practice, this process becomes a lot faster and with fewer mistakes.

Be there. This is simple yet sometimes forgotten. Missing a class will definitely hurt your chances of keeping up with the difficult topics later on in the semester, know this from experience. A book pales in comparison to Dr. Reitz’s teaching. He is able to energetically portray and explain difficult topics in a way that makes you want to try them out yourself. Do not hesitate to take advantage of the most valuable resource of learning, the professor himself.

Have fun! Strange to hear in a math course, I know. However, in this class, you can take everything you’ve ever learned and explain them in a whole new way. What is an even/odd number? How do you explain the binomial theorem? What is a statement? You will be able to learn the complexity behind the simplicity. It’s like finding a toy and figuring out how it works. Sometimes enlightening since you’re able to figure it out. Sometimes frustrating and you want to put the toy through a miller. At the end of the day, you’re definitely leaving the class with something more.

Yuyu chen, I totally agree, student “will be able to learn the complicity behind the simplicity” in this class. and like you said “don’t miss any class” and that’s a good advice because it is going to be hard to catch up especially in proofs.

“At the end of the day, you’re definitely leaving the class with something more.” I love your last statement that refreshes my thought about this class. First of all, we learned content knowledge, which we should master for this class. I would like to say that I learned a lot not only from the class itself but also from the Openlab, class work, and group project. Especially group project, I never done any group project before this class. I felt like I was not working alone which made me so happy about it. All of us came up with different ideas; we combined ours together as a whole in the end for our final product. I love this class which we could apply the way of thinking logically to some conjectures that we just came out of mind! It is kind of magic and interesting if we could take time and really think and work on it.

New student, this a challenging and an easy class at the same time. in one hand the class is challenging because this class is different then other math classes we take when first start college. In this class you are not just learning definitions and formulas and apply them to solve other problems but instead what you will have to do is prove some definition and concepts , so be prepared to do some proofs and remember every definition you prove in class like( odd and even numbers) because you are going to use them a lot in proofs. on the other hand, this class is easy if you just pay a full attention in class and follow Professor Ritz in what ever he does in the board, he explains the stuff really well. and don’t hesitate to ask equations and like Irania said the professor he is always happy to help and answer questions. and later on do the examples at home. that s what I did in this class, I had to focus all the time.

what I found challenging is the last topic witch is function because I never though a relation will be considered a function and when we made that transition the stuff got complicated, and it took me a while to understand it.

so that’s my advice to you guys and am sure you will do better in this class so good luck and study hard.

I agree that this class is quite easy if you pay attention. Also you should do all your homework. If you find something difficult, just keep doing the problems over and over again. The more you practice, the easier it becomes.

The first thing I would like to say thank you Prof. Reitz. 🙂 ! This is a great class that I learned a lot about proofs which also benefits me a lot for my Number Theory class. I wish Prof. Reitz told us that himself is a great professor, haha…

Seriously, I think being familiar with some terms might be helpful for succeeding in the class. For example, natural numbers N, integers Z, and real numbers R, which we use a lot when we prove any propositions. Also, it is always important to know that how crucial it is to do all the assignments. Prof. Reitz always gives us fair amount of homework assignments. Therefore, do the homework always. If you have questions, never mind! Ask questions! Prof. Reitz loves questions!

I think the most hard topic is Relation, which we need to identify if a relation is reflexive, symmetric, transitive,antisymmetric, and irreflexive. For some relations, they might fit only one of them; therefore, it requires us to be very flexible about the terms. When a relation belongs to all the terms, then we call it equivalence relation. I think practicing more on this topic will help out.

This class covers most of the proof methods. Therefore, it is an important class that each of the entering students to spend time on this course. Anything unclear, just read the textbook and try to work on the problem again. Always ask question if you still do not understand. Never over-think about a question which might show again on your test if you don’t study and get it done. Never do homework at the end of the semester which wastes the time for studying. I think these are all my suggestions for the entering students for MAT 2071. WORK HARD! PRACTICE MAKES PERFECT! 🙂

The main advice I would give everyone is to keep up with all assignments and practice as much as possible. Webwork and Open Lab count towards a large part of your grade so do not ignore them. This class teaches you a new way of thinking so it is necessary to practice as much as possible. Review logic manipulators, algebra, and anything you might know about sets beforehand. Try practicing abstract logic puzzles in your spare time. When working on the group assignment, make sure not to procrastinate. Later in the semester if you are behind on your group assignment there will be a lot of work. If you fall behind it will be a real pain to catch up. I personally loved this class. It allows creativity and ingenuity in mathematics you might not have had in the past. I hope that giving you concrete advice for the future will help you enjoy this class as much as I did.

I think the most important prior knowledge is knowing what the symbols mean. N is natural numbers, Z is all integers, and R is real numbers. We use them in most of the proofs, so its really important that you understand what they mean. Another thing you should know is what a one to one function is. It is one input gives exactly one output. We need this information when dealing with injective and surjective functions. I think most of the topics involving proofs are quite difficult. But it will be easier if you do all the homework and keep practicing the problems. There are also a lot of definitions that you have to remember, like odd = 2n+1, even = 2n. It’s really important you know them because you have to use them in the proofs. This class is really different from the other math courses, I like it a lot. The project that we did was really fun, it feels like a game rather than work. Hope you will enjoy this class too!

What is like to say to the following students taking Proofs and logic, is to do your homework on time and Practice Practice Practice, It is a fair amount of homework and it will help you pass your exams. If you have any questions ASK professor Rietz. He would be glad to help. Another thing is to be present in class, missing a class will definitely hurt your chances of keeping up with difficult topics later in the semester.

This is an easy class if you pay attention, yet it will be a challenge when it comes to proofs. The prior knowledge you need is basic algebra. There are no formulas to memorize, instead there are definitions that are needed to solve a proof.

What I found challenging during this semester was the topic involving functions and finding whether it was injective or subjective. This was only due to the absence of Professor Reitz, that tells a lot. When he is not there you will notice how his teaching captivates you to listen.

Overall that is my advice in passing proofs and logic, I really enjoyed taking this course and I’m sure you will pass and enjoy taking this course with Professor Reitz. Good Luck!

Daniela,

You are absolutely right. This class is easy if we pay attention to class and if we don’t miss any classes. I missed two classes and it was a lot that I missed. Also, Prof. Reitz is very kind and helpful.

I wish I knew that the proofs would have been this difficult and would have tried to expose myself to them earlier. I did hw but not as much as I could have. So my advice is to do the hw even if it is so much because it will help alot when you take your test. Another thing that really helped was being able to email the professor picruepres of how far ive gotten in a particular and receiving helpful tips/ advice to allow me to solve the problem myself. This really helped me because I went to three different tutors in the school but they were not helpful at all. I also didnt have time to go to the professors office hours so the last option the professor told us was to email him but try the problem first so he knows what we do and dont.

Rayan,

I agree with you. Homework was really helpful for the exam and also to revise because we might forget the concept of the problems. Unfortunately, you could not go to professor office hours otherwise it would be very helpful for you.

Dear future Profs & Logic Class,

At first, let me tell you about Prof. Reitz. He is great! I do not think you will have any problem with this class if you just focus him while is doing the lecture. Even if you are lost, do not hesitate to ask him questions. If you are shy to ask questions, email him. Trust me, he will reply you soon with a clear explanation. One better option for you to meet with him during the office hour. You will understand much better. I used to go most of his office hours for help.

I found the Counting topic was challenging and I believe that if you just study hard and practice, you will definitely become a master in that topic and the class.

Most importantly, you can team up with classmates and work in a group outside of the classroom. That will help you to success in this class.

I wish that I had been told in the start of class to help me succeed is that, this class is going to be fun, easy, but with a lot of work. The proofs, once you get into them, are quite challenging as you start them, but the main thing is to understand the basic theorems. For example theorems of even, odd, and Euclid lemma. These are just few of the many theorems but these, personally, were the most recurring. Furthermore, the trick to this class, in my opinion is, copy less, listen more. For example, don’t be so beat up on writing everything down, really pay attention to the lecture and what Prof. Reitz is saying and then just take pictures of the lesson. This way one can understand the concept of each proof, for as these proof scan get quite tricky pretty fast, but non the less, they are easy. Of course, if you pay attention. Also, last thing, don’t be afraid to ask questions. Professor Reitz is one of the few teachers that loves answering questions and does not get mad, so be completely comfortable in this class and you will learn.