1.-Don’t fear to make any kind of questions, instructors  will be pleased to help you  to find the answers

2.-Enjoy mathematics: the more you like it, the more you understand it

3.- If you pass MATH 100, you will be able to pass MATH 101 (because it is easier)

4.- Don’t worry too much about the grades, just focus in passing the courses (MATH 100 and MATH 101).

5.- Don’t be afraid of not understanding the topics at the beginning of MATH 100. It is one of the hardest first-year courses at UBC.

6.- Mathematics can look weird, but if you get some help  you will be able to understand (go to office hours)

7.-  Start assignments early. They take so much time to finish

8.- Study and focus on passing the course because you will not pass the Vantage One program

9.- Respect other people’s opinion. Perhaps,  you may be wrong instead of them

10.-Don’t procrastinate so much seeing memes like right now!!

Motivation

Have you ever considered the volume of water that covers the Earth? Or have you seen at the sky and wonder how many stars are in certain galaxy? Many scientists have wondered things like that, in fact the purpose of science is to give an answer to phenomena in the world and simplify the concepts to make them understandable for everyone in the world.

Now, let’s consider a galaxy and some astronomers that started their observations on that galaxy or better than that, think like those astronomers; if you wanted to know how many stars would be there applying an easy method, you should be wondering where to start. Perhaps, I would calculate the area of one star and the area of the target galaxy and I would use this data to determine the number of stars. However, the area of a galaxy or even the area of a star is not calculable because there are not regular polygons. We need an approximation to describe the area (a method that is not conventional).

Consider another situation where a group of geoscientists want to know the area of a tectonic plate but how can they measure the surface of an irregular shape? This is a challenging question because tectonic plates do not have any similarity with the common geometric figures for which we can easily calculate their area. How can you be sure about the surface of your country? It is another complicated issue that can be solved using mathematics.

Scientists and mathematicians have wondered these kinds of questions in the past and have come up with good approximations. Researchers and scientists started from previous knowledge. Since that scientists from different ages (and we will be scientists someday to join them all) began with very simple definitions, creativity was required to solve the problems they worked on.

For example, imagine yourself as Riemann (at this point is kind of weird since we already know what he did though). Let’s start by taking whatever irregular shape and divide it in small defined portions such as simple rectangles.  Now, we can make an approximation of the figure’s area by filling it with rectangles. The accuracy of the measurement depends on the number of rectangles used. The more rectangles you used, the more accurate your calculation will be.

Throughout the years, scientists have improved the methods to get an accurate value of areas, there is where the concept of integral appeared.

Names:

Loretta Li   26450163

Gustavo Loachamin    16367161

Mirkka Puente    22532162

For the third question you may want to recall the definition of continuity of a function at a specific point.

For 3.a. you only need to write the definition of continuity itself.

For 3.b. you may find useful to remember the formal definition of a limit for any function. Then, how can you rewrite this definition in epsilon-delta language?

For 3.c. the clue could be starting by writing the formal definition for each condition given at the problem (for example, write the formal definition of the limit for continuity of g(x) at a . Having also the formal definition of a limit in mind, you can relate inequalities each other. You would have to make a relation with the two deltas of the definition.

1. What distinguishes convergent sequences from divergent sequences

It is known that a sequence is a collection of numbers arranged in a specific way where there is a first element with or without a last element. There are two types of sequences: the ones that converge and the ones that diverge. We know that a sequence converges when it tends to only one value and it diverges when it doesn’t. This concept can be observed in the real world when, for example, we see a bouncing ball. Let’s observe only the maximum high the ball reaches in every rebound. We notice that the height is being reduced every moment the ball bounces. So each value of the height is decreasing in an ordered way and we can say that these values have a limit because there will be a moment when the height is zero. So this a sequence that converges to one number. But what if we think about the first cell in the world. We are not even sure about its form or size but we know it needed to reproduce itself in order to create a new living  being and the new living being needed to reproduce itself again, so the chain never ended giving as a result a variety of animals, plants and other living things. Surprisingly, this chain will never have an end because living beings will continue reproducing. In conclusion, we can notice that the number of living things continue growing to infinity, so we say the sequence is divergent.

Convergent Sequence

Divergent sequence

2. what distinguishes convergent series from divergent series.

It is known that a series is the sum of the elements o a sequence. Series can have a divergent behaviour when its partial sums do not have a limit or a convergent behaviour when its partial sums have a limit.

In order to understand series in a better way, you can imagine that you have a rich godfather who tell you that he is going to give you money every day. So the next day, he gives 50 dollars to you, the next day 25 dollars, the next day 12.5 dollars, the next day 6.75 and so on. Your godfather is so generous that he promises to give money not only to you but also to your next generations in the same order as he was giving money to you. The question is: do you think you will be rich? Will your grandchildren be rich? The answer depends on whether the series converge or diverge. If you say that the series diverge, then you will be rich. However if you say the series converge, you will only reach a limit of 100 hundred dollars.

My new blog is ready! 😀