What was difficult for me?
"For integers a and b with a ne 0, we say that a divides b if there is an integer c such that b=ac. We write a | b."
The section Proofs Involving Divisibility of Integers was difficult for me to understand at first. I understand the concept of dividing integers. The simple proofs did not give me too much trouble. However, as I continued to read, the problems increased in difficult. I had to read through the different proofs a handful of times in order to come away with a firm grasp on what they meant and the thought process behind solving them. What gave me the most difficult throughout the more difficult problems was just the way they thought through solving the proof using the different properties of being a multiple or a divisor. I believe with more practice I will come away understanding them more.
The second section we were assigned to read, Proofs Involving Congruence of Integers, was also difficult for me. I did not really understand the concept of being modulo. I need to read more into that, and I believe with some basic instruction I will come to understand it.
What was interesting to me?
Whenever I read sections like this, I'm fascinated as to how it was discovered. For example, the following from the reading:
For integers a,b and n > 2, we say that a is congruent to b modulo n, written a = b (mod n) if n | (a - b).
After reading through the following simple example, I found that so interesting. It also proved to be true. I don't quite see exactly how it helps, but I'm excited to learn how. Reading through these problems, I feel like I'm learning to think like a mathematician. It's a different way of looking at how to solve problem, and I feel that it will help me better solve statistics problems I am trying to code up.
"For integers a and b with a ne 0, we say that a divides b if there is an integer c such that b=ac. We write a | b."
The section Proofs Involving Divisibility of Integers was difficult for me to understand at first. I understand the concept of dividing integers. The simple proofs did not give me too much trouble. However, as I continued to read, the problems increased in difficult. I had to read through the different proofs a handful of times in order to come away with a firm grasp on what they meant and the thought process behind solving them. What gave me the most difficult throughout the more difficult problems was just the way they thought through solving the proof using the different properties of being a multiple or a divisor. I believe with more practice I will come away understanding them more.
The second section we were assigned to read, Proofs Involving Congruence of Integers, was also difficult for me. I did not really understand the concept of being modulo. I need to read more into that, and I believe with some basic instruction I will come to understand it.
What was interesting to me?
Whenever I read sections like this, I'm fascinated as to how it was discovered. For example, the following from the reading:
For integers a,b and n > 2, we say that a is congruent to b modulo n, written a = b (mod n) if n | (a - b).
After reading through the following simple example, I found that so interesting. It also proved to be true. I don't quite see exactly how it helps, but I'm excited to learn how. Reading through these problems, I feel like I'm learning to think like a mathematician. It's a different way of looking at how to solve problem, and I feel that it will help me better solve statistics problems I am trying to code up.
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