Altum Spectent

Essay Writing Tips

2022-11-11T21:12:00.000-06:00

When a professor assigns any type of paper, the first response for many is, "Oh, no! I can't do this! How many pages again?"

This, however, is not the way to think, as this will lead students to feel overwhelmed—that the paper will be impossible to write. Instead, the thought should be, "What can I write about? What am I interested in?" Then, once a topic is chosen, one shouldn't look at the whole—look at the parts: the introduction, the body, the conclusion; the paragraphs, the sentences, the words. If a good sentence is written, with appropriate words, sentence structure, and tense, then the only thing to do is make sure the same tense is used throughout the paper, and that words, sentence structures, and sentence lengths are not overused.

When this system is followed, it renders the writing process much easier, and less overwhelming. Once the paper is finished, the results can sometimes even surprise the author!

To summarize:

Look at the parts—not the whole

· Sections—introduction, body, conclusion

· Paragraphs

· Sentences

· Words

Ensure that the paper as a whole does not clash

· Same tense throughout the paper

· Make sure words, phrases, and sentence structures and lengths are not overused

If more guidance is needed than what I can provide, I have been informed by numerous professors that the Purdue Owl is one of the best writing help sites online.

Thank you for reading this post, and I hope that it helps both struggling writers and budding authors alike!

Beginnings

2022-04-30T22:31:00.000-05:00

To those who may see this sometime in the future, this is the beginning of my blogging experience. I had been wanting to start for some time, when one of my college professors made the suggestion that I really should start blogging. For those curious, I chose the title for multiple reasons:

It wasn't currently in use—a big plus
I wanted a title that would mean something—this does
It sounds prodigious

The title is in Latin, and when translated to English, "Altum Spectent" means "Always Aim High" or "High Regards." I believe one should always try to aim high—to set high goals or standards for life. This blog may end up being about one idea or many different topics, as I currently have possibilities to work on, but have not chosen one. I may not even have the right idea yet, but I'm working on it!

A little background would include the facts that I love to learn, excel in math (while enjoying it), can write professor-approved papers (enjoyment depends on the topic, the depth of the paper, and the point in the writing process I have reached). Moreover, my interests include classical music and books.

I hope that this blog is of interest to some, and that my posts can be of help to those who need it.

(For those who are wondering, this is the same as my "About" page!)

Test Preparation

2020-05-05T21:59:00.000-05:00

One of the most important things one will ever face in college, university, or high school is the basic test. Most of the time, your main grade is based on how well one performs on tests and exams administered by the professor. Some of the effects this may have on the student include stress, poor performance, and anxiety, which may, in turn, lead to cramming and possibly even health, fitness, and nutrition issues.

However, one does oneself no good by following this trend; on the contrary, if one makes a regular study habit, practices with friends or classmates, pays attention in class, reads the textbook, takes notes, or a combination of these suggestions, one will do one well in the long run. Sometimes, just taking deep breaths and remaining calm will help one perform much better on an exam than one would have otherwise. Another reason one should remain calm is that, quite often, the "self-fulfilling prophecy" will affect one and one's actions while taking a test. If one believes that one is going to fail, one is not going to try as hard as if one is confident in one's success. There are no guarantees that one will do better if one walks into a test confident, but there should be a higher success rate than otherwise. Self-Fulfilling Prophecy

"To expect defeat is nine-tenths of defeat itself. [It becomes a self-fulfilling prophecy. It is best to plan for all eventualities then believe in success, and only cross the failure bridge if you come to it!]" ~ Francis Marion Crawford

"Pessimism is not only unwarranted, it is also a self-fulfilling prophecy. If you think the cause is lost, it will be. No one works hard for a cause they think will lose." ~ Lawrence Reed

"Pessimism becomes a self-fulfilling prophecy; it reproduces itself by crippling our willingness to act." ~ Howard Zinn

It is also important that one has slept sufficiently at least the night before the exam, if not most nights

The Science of Speech

2020-05-05T13:26:00.000-05:00

Speech classes can be very frightening, for a myriad of reasons:

The professor may seem overconfident in your skills as a speaker
You may be introverted to a certain extent
You may not feel ready for public speaking
You may not feel that you have the right words
And many more...

However, you can overcome the situation! Often, simply having someone—such as your professor—believe in you can help you do so.

To avoid feeling as though you have the wrong words, it does help to choose a topic with which you feel comfortable and also to know something about it. Then, you can draft a speech at home and practice several times, and also make note cards with reminders about what to talk about and when. One big aid is having a manuscript speech written out, with which you are familiar, and extemporize on that. Then, even if you become stuck for words, you will still have your manuscript to fall back on for guidance.

Papers, Portfolios, and Polish

2020-05-04T23:48:00.001-05:00

Towards the end of the semester, many students are required to write papers, or revise one or more for their portfolio or final drafts. Moreover, some will also have to write a reflection on how their writing has improved over the course of the semester, including details about it, such as strengths, weaknesses, and more. If one isn't sure just how to go about this, start by looking at instructor comments on papers written over the course of the semester. This will often show one one's strengths and weaknesses, just as one can compare an essay written at the beginning of the semester to one written towards the end, and discover the improvement in the writing.

I personally find it easiest, once I have been given my topic, or have chosen my topic, to begin by putting my thoughts on the subject in the document, as well as my sources, and important information from those sources. Then, I start adding supporting information, rearranging my thoughts and paragraphs, and maybe a bit of the formatting I hope to use for the final draft. From there on, I generally only have to continue polishing the paper until, if ever, I am satisfied with the results. I would also make sure that my reference page is nearing completion, and add in most of the formatting at this point. Always go with a cover page—the more "professional", the better. This usually, if not always, has to have your name, the professor's name, the class, and the date. For inspiration, I usually look at what Word gives me as the "basic" options for cover pages or Google professional cover pages, and either adapt or create a similar cover page for my paper. Of course, you can edit the colors, fonts, pictures, sizes, and shapes of the elements available to make a fabulous cover page. Just don't go overboard! You're aiming for more than just the name and title on the page, but not going so far as to cover the page with pictures and shapes. There are some good examples here: Cover Page Examples. One of these cover pages will definitely help your paper stand out among the crowd.

Once you have your cover page, I like to add page numbers and a table of contents if the paper is longer and has headings. (By the way, if you are exploring different aspects of a topic, add headings; it looks better, more professional, and is a good organizing tactic.) Word may try to start your page numbers on the cover page, so you need to add a section break to start the numbering on the next page. If you want to add numbering "i, ii, iii..." to your table of contents and other pages that precede your paper and continue with "1, 2, 3..." when the paper commences, you will need to add another section break in between the two areas, and make sure that the header and footer do not continue from the previous section. The numbering is also highly editable: coloring, font, background, shape. Do make sure that you start it at "1" from the first page of the section, though, or it may include prior pages in the count. The table of contents can be automatically inserted when using Word, and you can update it to include headings (levels 1-3) and page numbers that are added after the table is inserted. (As a side note, the page numbers you add will be used when creating the table of contents.) This is much easier than manually creating your own.

As for your reference page and in-text citations, these are mandatory if you cite any sources. Plagiarism is classified as cheating, even if you just forgot to include the source, and will result in a failing grade on the paper. Word will automatically create a citation for you in the correct format if you fill in the necessary information. (Some of the formats are not to the latest standards, but they are very similar, and professors usually do not care if there is a slight discrepancy in the format.) It includes the main two, APA and MLA, but also includes several other lesser-known formats as well. Although these formats are all supposed to be different, the main difference is the citations; the actual paper itself is usually one-inch margins, single- or double-spaced (depending on the professor, and whether this is a professional report), 12-point font, Times New Roman.

If you get to submit both a rough and a final draft, definitely get your professor's feedback and incorporate it in the paper. This will make your paper better, and professors do appreciate those students who take their advice and instruction when writing their papers. (They also appreciate a professional-appearing document.)

Accounting Tips and Tricks

2020-05-04T22:28:00.001-05:00

For all those of you who can't tell your debits from your credits, or otherwise have difficulty with accounting, hopefully this post will be able to help you out.

We'll start with the basics, at the very beginning. Debits are placed in the left column; credits in the right. The three main classifications for accounting are Assets, Liabilities, and Stockholder's Equity, which all must be in balance in the Accounting Equation, where Assets (A) = Liabilities (L) + Stockholder's Equity (SE). Stockholder's Equity can also be referred to as Owner's Equity (OE); generally the difference is referring to the type of company: corporation or sole proprietorship.

Debits increase regular assets; decrease regular liabilities; and decrease regular stockholder's equity. However, there are some times where this is not the case; for example, depreciation is a contra-asset account, meaning it belongs with the assets, but it is decreasing, or against, the assets, so debiting the account actually decreases it. Same with Stockholder's Equity accounts—any and all expenses are debited to increase them, credited to decrease. Moreover, Stockholder's Equity accounts can get much more confusing—there are actually contra-revenue accounts, such as Sales Returns, allowing for any returns customers may make.

The next topic one generally learns about are journal entries; every entry must have at least one debit and one credit, although it could have more of one or both, as long as the two columns end up being equal. Although eventually one will get to use software that will do most of the heavy lifting, one usually starts out learning the whys and wherefores of the subject, so for the first step, one would "take the day's receipts" and "journalize" them. This basically means transferring the sales, cash, receivables, or other accounts dealt with by the company from the receipts or notes and officially adding them, as an entry, to the general journal. Once that is complete, one will take the individual accounts, and post them to their specific "T-account" in the general ledger; in addition, one will often put the general journal page number next to the transaction entry in the t-account, and the account number from the general ledger next to the account entry in the general journal. From there, the financial statements will be prepared at the end of the period.

There are four main financial statements with which accountants should be familiar: the income statement, the statement of retained earnings, the balance sheet, and the statement of cash flows. There are other financials which are not as important, and some other names by which these may be known, but these are the most useful. These financials are all interrelated, and they flow through onto one another when one is preparing them. The income statement presents how much income (or loss) was made by the company after expenses are deducted from revenues; the statement of retained earnings, a measurement of the change of equity, starts with the beginning retained earnings, which are monies kept within the company, and adds net income (or deducts net loss) and deducts dividends to arrive at ending retained earnings; the balance sheet is considered a snapshot of a point in time of the company's assets, liabilities, and stockholder's equity (which is where retained earnings flows through); and the statement of cash flows attempts to give a depiction of the cash receipts and disbursements made by a company, and why the company's ending cash balance is what it is.

Of these statements, the income statement, the statement of retained earnings, and the statement of cash flows are presented at the end of a period of time, often the end of the month, quarter, or fiscal year. The reason for this is that they represent a change in the value of an account or of the way in which the value of an account was generated. The balance sheet shows the balances of the main accounts on the books of the company on a specific date, usually the end of the period, whether that be month, quarter, or year, but it does not show the change over time.

Another important distinction which must be drawn is that a company may have different calculations for different accounts depending on the parties to whom the information is being presented. The company might have one number on their own books, another number for investors and the general public, and yet another value for the IRS. Yes, a company's "books" and "tax" information are very different most of the time, as the IRS asks for, and, indeed, requires, one set of calculations made under strict guidelines, while the Financial Accounting Standards Board (FASB) has another very specific set of Generally Accepted Accounting Principles (GAAP) for the public. As if that isn't enough, certain parts of the statements are different if presented internationally, as instructed by the International Accounting Standards Board (IASB) and their rules, International Financial Reporting Standards (IFRS). However, one generally does not have to learn about all this in the same class.

One website that looks as though it could be quite helpful to struggling accounting students—Accounting Coach. Although some features of the site are only available to paying customers, I believe that mainly the necessary accounting information is free, and additional helps may be what actually would cost you.

Frequently Asked Questions

2020-05-04T19:49:00.002-05:00

Hello! I have a few questions I get in the comments quite frequently, and I will be answering those here. I will also be addressing a couple issues that crop up quite a bit. Although this is a post, I am creating an FAQ page, as well, that will include these questions, and any others you may send my way in the future.

FAQ

Does your blog have a contact page?

Yes, it does! Currently, it is located here: Contact Form. This is an entirely anonymous form, and while it does have the option to add name and email, this is ONLY required if you would like a personalized response directly to you.

How can I contact you?

As mentioned before, I have a contact form; I also would love to be contacted through twitter; discord is an option; and there is a contact chat option located in the bottom right corner of the blog.

What site hosting do you use?

I am currently using Google Blogger, a free blogging service by Google, which may not be the best by any stretch, but the amount that I blog definitely does not justify anything else at this time.

What do you have for site security?

I am just using the Google blogging software; I do not have any additional security beyond what Google provides.

How do you filter comments?

At this time, I have Blogger set up to notify me whenever I get a comment, and I must read through everything before any comment is published.

Can I share strategies, posts, or guest authorships?

I would absolutely love to share information, or see what others have to share with me! However, I do need some contact information to communicate. If your comment or contact form is anonymous, I cannot reach back out to you.

Can you send me an email later?

Again, I would love to be able to contact you back about your requests, but I do not have the ability to respond directly to an anonymous comment; the best I can do is respond to your comment on my blog, unfortunately.

Do you have social media?

Yes! My twitter account is here: AltumSpectent.

How can I follow you?

Here is the link to follow me by email: Follow; for other feed readers and blog compilers, feedburner has several options available.

Issues

At this time I would like to make a couple of requests regarding certain issues I have noticed in the past:

Please do not make a comment unless it pertains to the content of the post. If you have something you would like to add, something that should be brought to my attention, or anything else you feel you should submit, please use the anonymous contact form here: Contact Form. However, if it genuinely relates to the post, feel free to comment all you want!
This request relates to the last issue and some of the FAQ's, but I would like to mention it specifically: If you want to ask me anything about my blog, such as security, hosting, or comments, please contact me using the Contact Form.
Please, if you feel the need to mention the quality of my grammar, or anything of that nature, use the contact form. That is what it is there for, and I will see it and I will be able to respond directly if you leave an email.
If you want me to contact you, please use the contact form and please leave an email address at which you can be reached. I do not plan to use the information to spam you, and I do not mind replying to a "burner" email, as long as the information you request will get back to you.

I hope these FAQ's help to answer a few of your burning questions and that you can help me by using my contact form. If you have any other questions, please use the contact form, or comment below; this post is a perfect opportunity! I will be creating an FAQ main page, and any additional questions will help fill it out!

Systems of Linear Equations

2019-03-22T21:56:00.002-05:00

I'm back! Sorry for the tardiness, but college students never have much extra time on their hands.

Anyway, today's post will be a mathematical review; coming directly from a recent tutoring session in which I helped a student with systems of linear equations. Systems of linear equations can be solved by using either the substitution method, the addition method, or the graphical method. Sometimes more than one method is required, especially for systems of three equations, each with the same three variables. Personally, I prefer the addition and substitution methods, but the graphical method is fine, too.

Say we are given the following system of linear equations:

This is very simple and straightforward example. We can solve this easily using the addition method, which would simplify to 3x = 6, which would further simplify to x = 2. Using this result, we can solve for y: (2) - y = 1 à 2 - 1 = y à y = 1. Or 2(2) + y = 5 à 4 + y = 5 à y = 1. Our answers, therefore, are x = 2 and y = 1, or an ordered pair of (2,1).

If we decided to use the substitution method, on the other hand, we would begin by solving for a variable in either of the equations. I'll solve for y in equation 2: x - y = 1 à y = x - 1. Then we substitute this in equation 1 for the variable y: 2x + (x - 1) = 5 à 3x - 1 = 5 à 3x = 6 à x = 2. The rest of the answer is the same as that already used for the addition method.

The same method applies if we have a system of three equations, each with the same three variables. There will just be more steps involved. We will solve the following example:

I will start with the substitution method, solving for z in the third equation. z = 3x - y - 10. Next, we will substitute this value for z in our other equations, before using the addition method. If we do use the addition method first, as it is tempting to do, we will still end up with a value for y. So that will give us 2x + 2y - (3x - y - 10) = 4, which simplifies to -x + 3y + 10 = 4 or -x + 3y = -6. In our second equation, we get x - 2y + 4(3x - y - 10) = 5, which, after simplifying, results in x - 2y + 12x - 4y - 40 = 5. After further simplification, we find 13x - 6y = 45.

In order to ensure that we can cancel one of our variables, I will multiply the entirety of the first equation by 2. Our result being -2x + 6y = -12. And now, we can go ahead and use the addition method:

Which gives us the conclusive result that x = 3. Taking that answer, we can substitute that value for x in either of the most recently derived equations. We will use that derived from the original equation two. 13(3) - 6y = 45 à 39 - 6y = 45 à -6y = 6 à y = -1. And finally, we can use those values in the equation solved for z in the first step to find a value for z. z = 3(3) - (-1) - 10 à z = 9 + 1 - 10 à z = 0. Our ordered triplet, then, is (3,-1,0).

I hope this finds those that may need it, and that it helps them to understand better how to find the intersection point, or solution, to a system of linear equations. You can contact me through my ANONYMOUS contact form: Anonymous Contact Form—it does have a place for a name and email, BUT those are NOT REQUIRED—the one caveat is that you might not be able to get a response.

Thanks for reading! Please follow here if you are interested in receiving future posts: Follow! If you want it sent directly to your email, please click here: Follow by Email.

Parabolic Problems

2018-10-11T22:37:00.000-05:00

Another problem I have seen lately is that of parabolas and symmetry, as well as that of intervals, domains, ranges, and other graphical dilemmas.

If one is asked to define the interval over which a function is increasing, decreasing, or remaining the same, the answer is always (x₁, x₂). One never uses brackets when referring to an interval! However, if one is asked to define a domain or range, the answer could include one or more brackets: (x₁, x₂], [x₁, x₂), or [x₁, x₂] if referring to the domain; (y₁, y₂], [y₁, y₂), or [y₁, y₂] if referring to the range. (x₁, x₂) and (y₁, y₂) can also be used to describe the domain and range, respectively, in some cases.

A function is said to be increasing if the y-values are getting larger, decreasing if they are getting smaller, and constant if they are remaining steady. The domain of the function is the entire group of all the x-values for which the function is continuous, while the range is the entire group of y-values for which the function is continuous.

The bracket is used when the function is continuous over the requested domain or range, but in the case of infinity, the parenthesis is used, instead. If the function is discontinuous, the parenthesis is used.

y = x² + 6x + 7

Given the equation y = x² + 6x + 7, one can not immediately deduce what the function looks like, except that it should be a parabola.

This is where the vertex form of the parabola comes in:
y = a(x - h)² + k.
To get the equation in this form requires a little bit of thought. We need the original equation in the

form of a perfect polynomic square—in this case y = x² + 6x + 9.

Start with the original equation: y = x² + 6x + 7. Add parentheses: y = (x² + 6x + 7). In this case, add 2 inside the parentheses, and subtract 2 outside the parentheses: y = (x² + 6x + 7 + 2) - 2. This allows the function to have the same value as it had originally, while also putting it in a more convenient form. Next, factor the function: y = (x² + 6x + 9) - 2—y = (x + 3)² - 2. This—y = (x + 3)² - 2—is the final "vertex form" of the equation; we can now find the vertex, see whether we have a positive or negative parabola, which will also tell one whether there is a maximum point or a minimum point.

Looking at the equation: y = (x + 3)² - 2, there is no "sign" before the parenthesis—y = _(x + 3)² - 2, meaning this is a positive, upward-facing parabola, with the vertex at the minimum. Moving on to the next item of interest—y = (x + 3)² - 2—the x-value of the vertex is always the opposite of the number in the parentheses; in this case, x = -3. And lastly, the equation can give us the y-value of the vertex: y = (x + 3)² - 2; the y-value of the vertex is always equal to the number to the right of the parentheses—if there is no number there, y = 0. However, in this case, y = -2. This gives a resultant vertex of (-3, -2)

The x-value can also be found using the equation: x = - ^b⁄_2a with the quadratic formula.

If we had had y = x² - 6x + 7, instead, the function would have simplified to y = (x - 3)² - 2, with a positive, upward-facing parabola, with the vertex again at the minimum—this time at (3, -2), however.

If a question asks about symmetry, the equation of the line of symmetry in a vertical parabola—as seen in the example—is equal to the x-value of the vertex. In the example above, the axis of symmetry is found at x = -3. For a horizontal parabola, the axis of symmetry would be found at the y-value of the vertex.

Questions asking about whether a function is symmetrical about the x-axis, y-axis, or origin, are generally simple as well. If the function is mirrored, or looks the same, on both sides of either the x-axis or y-axis, it is symmetrical. To be symmetrical about the origin, however, the function must look the same across the origin diagonally. If it looks one way in Quadrant I, it must be mirrored across, flipped, into Quadrant III; not either of Quadrants II or IV next to it—it has to be the quadrant directly across the origin—diagonally.

If you are ever needing an online calculator, maybe one that's more helpful than just typing your question into the search bar, I have found Mathway to be quite useful when I don't have my calculator with me!

I hope this post is helpful to those who may be struggling with this—especially with midterms approaching, and for some, almost over; however, if any clarification would be of assistance, please let me know via my contact page found here: Contact Me. Thanks for reading! If this was of assistance to you, please share, follow me, or let me know through the comments section below.

Chemical Mixture Problems

2018-09-12T23:13:00.000-05:00

Recently, I tutored a few students in math, and they were having the same problem: How to solve a chemical mixture equation?

Chemical mixture problems can pretty much always be solved with the equation: p₁(v₁) + p₂(v₂) = p₃(v₁ + v₂), where "p" refers to the various percentages of the chemical involved and "v" refers to the various volumes of the chemical involved. The question should give either all three percentages as well as one volume, or both volumes as well as two percentages.

When solving a problem such as this, it is unimportant whether the percentage is listed as a number such as 75, or a decimal, such as 0.75, as long as the same method is used throughout the problem.

Here is a sample question below:

A chemist needs 150 milliliters of a 50% saline solution but has only 18% and 78% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

So, we can start equating variables with values: p₁ = 18, p₂ is 78, p₃ = 50, and v₁ + v₂ = 150. Solving for v₁, we have v₁= 150 - v₂. Thus, 18(150 - v₂) + 78(v₂) = 50(150). After simplifying, we have the following: 2,700 - 18v₂ + 78v₂ = 7,500. Simplifying further: 60v₂ = 4,800. Our answer? v₂= 80. However, we still need to find v₁, so we substitute v₂ back into our equation for v₁, so v₁ = 150 - 80. Our final solution leaves us with v₁ = 70 mL (of the 18% solution), v₂ = 80 mL (of the 78% solution).

Now say that we have the same question, given different values:

A chemist needs a 50% saline solution but has only 18% and 78% solutions available. If he has 70 mL of the 18% solution, find how many milliliters of the 78% that that he needs to get the desired solution.

So, again, we have very similar variables: p₁ = 18, p₂ is 78, p₃ = 50, and v₁= 70. Thus, our equation looks like this: 18(70) + 78(v₂) = 50(70 + v₂). After simplifying, we have the following: 1,260 + 78v₂ = 3,500 + 50v₂. Simplifying further: 28v₂ = 2,240. Our answer? v₂= 80 mL, and v₁ + v₂ = 150 mL total.

The one last type of this problem that one may see is that of the missing percentage:

A chemist can make a 50% saline solution with 70 mL of an 18% solution and 80 mL of a saline solution with an unknown percentage. What percent salinity does the second solution have?

Here we have the following variables: p₁ = 18, p₃ = 50, v₁= 70, and v₂= 80. Our equation is 18(70) + p₂(80) = 50(70 + 80). Simplifying: 1,260 + 80p₂ = 50(150). After another round of simplification, we have: 80p₂ = 7,500 - 1,260. And again: 80p₂ = 6,240; leaving us with the result that the percent salinity of the second solution is as follows: p₂ = 78%.

For those who may need more math help than I can provide, Khan Academy has tutorials on many subjects, math among them, from Kindergarten all the way up to higher-level math such as Calculus!

I hope that this post is helpful to both aspiring engineers and struggling mathematicians alike. If any clarifications would aid understanding, please let me know via the comments section below or my contact page. Thanks for reading!