The Chemistry Degree Program at Loyola University Chicago

The Chemistry Degree Program at Loyola University ChicagoThe course of a Chemistry at Loyola has some common traits. While they are all taught at the same time, each of them is taught slightly differently in terms of pedagogy and subject matter. While some courses require attendance at class at the beginning of the semester, most require that students register for classes on a full-time basis in order to take up any time during the semester.Chemistry courses at Loyola are taught by both professors and graduate students. In fact, more than two-thirds of the students at Loyola are students in their first year of college. There are two divisions to the Chemistry department: Chemical Sciences and Applied. Chemical Sciences concentrates on the study of chemical properties of substances, while Applied Sciences concentrates on the analysis of physical properties of organic compounds.To begin the study of Chemistry at Loyola, students must first choose a major. The chemistry major at Loyola is limited to the study of chemical properties, which is used as a science in the area of chemistry. The core requirement for this degree is a two-year course in laboratory science or research.When students decide upon a major, they then must choose between the bachelor's degree in chemistry and the master's degree in chemistry. The chemistry majors are enrolled in two-year programs, whereas the master's degree students can work toward a four-year program. In order to determine a major, students will need to look at the coursework required to earn a bachelor's degree. Once they know what they want to study, they will need to narrow down their possible majors in order to work towards their chosen major.Those who wish to study at Loyola will likely need to take up a course from the pre-professional degree program, which covers subjects such as pre-medical career planning, personal finance, business management, and leadership. Thisis a good choice if you are not sure how you would best pursue a career in chemistry. Students that are studying at Loyola do not have to worry about getting a masters in the sciences or any other degree unless they would like to get a PhD. While there are no mandatory courses for the chemistry degree, the departments do offer a variety of pre-professional coursework in the areas of biology, chemistry, and physics. However, for those interested in pursuing further studies, students should try to enroll in a pre-professional degree program, which will give them the experience needed to graduate.The pre-professional classes at Loyola are a necessary part of the chemistry degree. You will find several topics in the pre-professional curriculum that cover concepts such as legal rights, ethics, and business. A large number of students are unable to go back to college, but without the proper preparation, they may not be able to get a degree in chemistry. It is important to note that while pre-professional courses are helpful for some, they do not guarantee that students will receive a satisfactory degree. Instead, it is up to the student to go through the pre-professional process.As mentioned, Loyola is one of the few colleges in the nation to offer a pre-professional degree in chemistry. If you are a good student, take advantage of this opportunity, and make the most of your education, you will be well-equipped to proceed with a degree. Make the most of your college experience by focusing on the areas that are important to you and ensuring that you get the most out of your time spent at Loyola.

A Student Review of Brigham Young University

A Student Review of Brigham Young University The tutors behind Varsity Tutors are not just here to teachtheyre sharing their college experiences as well. Abigail received her bachelors degree in Spanish translation from Brigham Young University in 2012. She specializes in a number of levels of Spanish tutoring, among other subjects. See what she had to say about her experience attending Brigham Young University: Describe the campus setting and transportation options. Abigail: Brigham Young University is a very large walking campus, to some students chagrin. I walked for most of my time as a student and planned my commutes and my class schedule accordingly, but I also rode a bike for a couple of years which was very practical. There are large student parking lots on the perimeters of campus, but they were usually always full during popular class times and you typically still had a substantial hike on foot after you parked. The city of Provo does have a bus system, but I never had occasion to use it. How available are the professors, academic advisers, and teaching assistants at Brigham Young University? Abigail:Very available, I wish I had used this resource more. Professors are open about their office hours and I always felt comfortable seeking out a teacher in their office. How would you describe the dorm liferooms, dining options, location, socialization opportunities with other students? Abigail: Social! Dynamic! Family style! Fun! At BYU you can choose dorm style or cooking style apartments. I chose the latter because I wasnt a fan of the cafeteria diet, but there certainly are options for that. Since this is a church school, student resident life is organized by into congregations as well, and that group dictates most of the social life/activities you are involved in. Which majors/programs are best represented and supported at Brigham Young University? Abigail: Im not sure what major/program is most popular at BYU, but they do have a prestigious language program largely due to the fact that most of the student body are LDS and many of them have served volunteer foreign language speaking missions. I studied Spanish Translation, and the program did a thorough job of orienting us toward the world of opportunities in that field and there was always a wealth of experience available within an international church. How easy or difficult was it for you to meet people and make friends as a freshman? Does Greek life play a significant role in the campus social life? Abigail: It is extremely easy to make friends as a freshman. There are always activities in your building and in your ward that connect you to the people you live around and go to church with. I was part of Sigma Delta Pi as part of my Spanish degree, but there were never any events or meetings associated with my membership in that group. Your ward plays a stronger, more significant role in your social life than a fraternity or sororityin fact, I dont know of any fraternities or sororities on campus. How helpful is the Career Centerand other student support services? Abigail: The Career Center is always buzzing and there is an actively updated job board with campus job postings. This information is also available online, and I was always able to find a campus job. There is also an annual job fair with many reputable companies who come to recruit. BYU students are known for being good students, good citizens, squeaky clean, honest, hard working, and cultured. How are the various study areas such aslibraries, the student union, and dorm lounges? Abigail: The BYU library is enormous and mostly underground. There is always a place to study whether you do better in large space with many people studying quietly or more secluded cubicles or nooks and crannies that you can sneak away to. There are also many computer labs. I didnt have a computer for most of my time as a student and I was always able to find one to use on campus as well as to print. Describe the surrounding town at Brigham Young University. Abigail: Provo and Orem are fun college towns with malls, movie theatres, restaurants, indoor rock climbing, museums, water parks, canyons, mountains, and the Provo River. I was around south Provo and Orem almost as much as I was on campus. How big or small is the student body? Were you generally pleased or displeased with the typical class sizes? Abigail: Its a huge student body. 30,000 plus students. I had some very large lectures with hundreds of people, but I also had small classes with only a dozen people. I loved both experiences. Describe one memorable experience with a professor and/or class. Perhaps one you loved the most or one youregretthe most. Abigail: Every Tuesday morning the whole campus shuts down at 11:00 for a campus wide devotional or forum. You can attend these devotionals in person in the Marriott Center, or watch them broadcast throughout campus. Rich, inspirational, intellectual messages are delivered to the student body each week. Check out Abigails tutoring profile. The views expressed in this article do not necessarily represent the views of Varsity Tutors.

What is it Like to Attend North Carolina State University at Raleigh

What is it Like to Attend North Carolina State University at Raleigh The tutors behind Varsity Tutors are not just here to teach theyre sharing their college experiences as well. Laila received her bachelors degrees in Spanish and public relations from North Carolina State University at Raleigh. She is currently an online tutor specializing in Spanish, English, and ESL/ELL. See what she had to say about her experience at North Carolina State University at Raleigh: Describe the campus setting and transportation options. Laila: North Carolina State University has a fairly large campus. Its student body population was just under 30,000 when I studied there. This was much larger than my small hometown of 500 people. Such a large student body may sound intimidating for some folks, but once you make friends and get into your core classes, it feels much smaller. Because it is the size of a small city, transportation was reliable and constant. You could certainly walk to your classes, or take the Wolfline bus system, which ran day and night. Some students also biked, and some drove cars, but the bus system was clean and consistent. I never felt unsafe on the campus, but as with any populous area, students should expect to exercise caution and be smart to help deter avoidable security incidents. How available are the professors, academic advisers, and teaching assistants? Laila:The availability of the professors, of course, depended on the particular professor, but most of them were pretty available for the students. All professors had office hours that they either honor themselves, or that their TAs would honor. The availability of the academic advisors also varied. I changed my major once and added on a second major during my time at North Carolina State University, so I had more academic advisors than the average student. I didnt find my academic advisor for psychology (my initial major) incredibly available; I got the impression that he was very focused on his research, and I felt I was marginal to him. In contrast, my advisor for communication (my second major) was extraordinarily available and very friendly, so it really depends. I would suggest to any student to take ultimate ownership of and responsibility for your academic success and to make your academic priorities that of your professors. Also, form relationships with professors and depart ment staff outside of your advisor. How would you describe the dorm life rooms, dining options, location, socialization opportunities with other students? Laila:North Carolina State University has a lot of dorms, since there are so many students (I lived on the 10th floor of a tower dormitory my freshman year). Of course, those with seniority have first pick of where to live, and most freshmen are placed on Central Campus to help them become acclimated to campus life and help ensure their success, which I think is good. There are also off-campus apartments that you can live in, either with friends, or with other students (many apartments have roommate matching options). For food, there are two dining halls on different sides of the campus for convenience. There are also many restaurants on the two main streets surrounding the university, as well as convenience stores on campus with basic food items like milk, cereal and of course, Ramen Noodles! There are plenty of socialization opportunities, especially during the first few weeks of the semester. A lot of student groups plan events and the university sponsors events, too. There are also a ton of student organizations (around 300), and if you dont find one you like, you can also start your own! Theres a department in the student center whose whole purpose is to support student organizations, so youre in good hands. Which majors/programs are best represented and supported? Laila:North Carolina State University is probably best known for its engineering school, as well as its research in the hard sciences. However, it also offers almost any major you could think of. I had two majors: Spanish and communication, with a concentration in public relations. I chose Spanish because I had fallen in love with the language and found myself very passionate in my pursuit to master it, and I later added on public relations because I enjoyed both writing and working with people. I think there was a good deal of support for both of my degree programs. For example, with Spanish, the professors were always sending out opportunities to help further students linguistic and cultural fluency, both locally and internationally. For public relations, there were local societies that afforded many networking opportunities, and also a semester-long internship built into the plan of study. I took advantage of these opportunities in a number of ways. I studied for a semester in Puerto Rico at a school with a good reputation for communication studies. I also completed three internships: one with a Latino advocacy nonprofit, where I interviewed Spanish-speaking lay health advisors; one with a state government entity, where I created marketing materials and translated information to Spanish; and one with an advertising agency, where I provided research and client support for the public relations department. I do think North Carolina State University does a good job of providi ng support and information about opportunities; ultimately though, its up to the student to take advantage of them, so dont be afraid to dive in! How easy or difficult was it for you to meet people and make friends as a freshman? Does Greek life play a significant role in the campus social life? Laila:I found it fairly easy to make friends as a freshman. North Carolina State University breaks the incoming freshman class into orientation groups, so many of the friends that I carried throughout my undergraduate career were those from my orientation group. Having an outgoing, or at the least, friendly, personality also helps. You can also make friends from any student organizations that you become a part of as well, so I would definitely encourage getting involved, especially based on your interests. Join the Spanish club, a Bible study group, or an engineering society like NSBE, or even start your own group. Many students later join a fraternity or sorority, which is also a way to make friends, network, and engage in diversions. I would say that Greek life plays as big of a role in your life as you allow. Many students go Greek, while others opt for different activities. Either way, theres always something to do on campus. How helpful is the Career Centerand other student support services? Laila:I was one of the students who visited the Career Center several times, especially in my junior and senior years. I found them very helpful in critiquing my resume or cover letters, and even offering career advice. I would definitely recommend that all students start visiting the Career Center at the start of their junior year, if not sooner. They can give you a lot of tips on how to job search and tell you about recruitment events. Many companies do recruit on campus engineering firms, nonprofits and international companies, so there are lots of opportunities presented to students. How are the various study areas such aslibraries, the student union, and dorm lounges? Laila:The great thing about the library was that it stayed open 24/7 (though I think now they close at 11 p.m.). If you had to study late, there were campus-sponsored escorts that would take you to your dorm. The main campus library, D.H. Hill, has 4.5 million items (yes, million!). It also has cool things like microfiche of The New York Times editions from the 1800s, a digital media lab, plenty of computers, and private study rooms. Unless its around finals, finding a place to study is easy to do in the library. During finals, you may have to look a little longer, but youll still find somewhere to study. Theres also now an additional library that has been built since Ive graduated, which Im told is very nice. Some people also study in the campus lounges, but that can be hard because they are also used for cooking, watching television, and playing games, so I would definitely recommend the 10-story library over the lounge. Describe the surrounding town. Laila:Raleigh is a city that feels like a large small town, but theres plenty to do. There are museums, the state fair in October, concerts, plays, basketball, football and hockey games, restaurants, 5Ks, trails, etc. There are also other colleges nearby in Raleigh (Shaw, St. Augustines, Meredith, Peace), and Duke, NC Central, and UNC Chapel Hill just down the road. Personally, I didnt do much exploring of the actual city until after I graduated, but a lot of students go downtown for fun. How big or small is the student body? Were you generally pleased or displeased with the typical class sizes? Laila:North Carolina State University has a large student body population, which was just under 30,000 (undergrad and graduate students) when I studied there. Such a large student body can be intimidating for some folks, but once you make friends and get into your core classes, it feels smaller. General education classes can have as many as 300 or more students. The classes for my majors, though, typically had around 20-30 students, sometimes even as few as 10, depending on the course. I wasnt really affected by the class sizes, even for the larger classes. I was never shy about asking questions, utilizing office hours, and introducing myself to the professor so that I wasnt just another face. Describe one memorable experience with a professor and/or class. Perhaps one you loved the most or one youregretthe most. Laila:Professor Gray was probably the toughest instructor among those who taught Spanish, and I had her for my Spanish 201 class as a freshman. I did fairly well in that course, and I even tutored others. I enjoyed her because she challenged us, but a lot of other students avoided taking her classes. Since Spanish was my major, I took 300- and 400-level Spanish courses, and one semester, I decided to take another, more in-depth course that she taught: Business Spanish. I did horribly in it! It was not any easy class, by any means, and she was an instructor who gave students exactly what their work merited. Ever relentless, I didnt let it shake me. Once I had a better understanding of Spanish, its structure, phonetics, and more vocabulary, I took another business Spanish course, also taught by Professor Gray. The second time, I understood far more, and I also utilized her office hours whenever I needed to. It paid off when I earned an A+ for the semester! I have the deepest respect fo r Profesora Gray. She remains one of my favorite teachers from North Carolina State University, and I even go back and speak to her classes (in Spanish, of course!) as one of her star student examples. Check out Lailas tutoring profile. The views expressed in this article do not necessarily represent the views of Varsity Tutors.

How To Improve Your GMAT Essay

How To Improve Your GMAT Essay The GMAT has one 30-minute essay: the Analysis of an Argument prompt. It has a pretty basic formula, and yes, were going to walk you right through it. Instead of arguing your belief, you will actually critique another authors point. However, this essay still requires the classic, 5-paragraph setup. In the first paragraph, youll need to take a stance that the authors argument is either logical or illogical. Next, you will use 3-4 paragraphs of points to confirm your stance. Finally, youll put together a strong conclusion to sum it all up. Example prompt:The Awesome Energy Riders have become an extremely popular toy line for the ACME Co. Management. Hollywood Pictures thinks that this success will translate to the silver screen and has bought the rights of the Awesome Energy Riders to make four pictures. Directions:Discuss how well reasoned you find this argument. In your discussion, be sure to analyze the line of reasoning and the use of evidence in the argument. For example, you may need to consider what questionable assumptions underlie the thinking and what alternative explanations or counterexamples might weaken the conclusion. You can also discuss what sort of evidence would strengthen or refute the argument, what changes in the argument would make it more logically sound, and what, if anything, would help you better evaluate its conclusion. Before you jump into writing, try to come up with 3-4 high-level reasons why this argument is logical or illogical. Below you will find a very solid guide for writing your essay. In fact, this could be used for nearly any Analysis of an Argument essay. First paragraph Firmly state if you find the argument logical or illogical. For example: The argument to produce four Awesome Energy Riders pictures is very poorly reasoned. Based on the information given, it is nearly possible to conclude that the toy lines success will translate into film success especially the success of four films. Second paragraph Remember that you are not arguing whether or not these films will be successful (although that can come into play), but rather you are arguing if the prompt given can determine if the films will be successful. In this paragraph, you could make the point that the prompt makes false assumptions, the most obvious of which is the assumption that toy success leads to film success. You could write about how the G.I. Joe toy line was one of the most successful and popular toy lines, but the movie was a gigantic flop. Additionally, many popular toy lines are derived from movies (like Disney films), but rarely do Hollywood studios base films off of toys. Toy Story is a prime example because the toys were derived from the film and not vice versa, which led to success on both fronts. The prompt falsely assumes that the success can translate, but previous history indicates it will not. Additionally, make sure to understand the distinction between examples and points.This argument makes false assumptions, is a point. The unsuccessful G.I. Joe film is an example to support that point. Make sure you have a couple of examples to support each point you make. Sure, you could write an entire 5-paragraph essay outlining G.I. Joe in one paragraph, Toy Story in another, and a third, similar example in the next one to all support the false assumption point. However, thats not nearly as creative as having 3-4 legitimate points and examples to prove all of them each of which prove that the prompt is illogical. Third paragraph The argument ignores critical factors. For instance, if James Cameron is writing this film and it has a $500 million budget and star-studded cast featuring Leonardo DiCaprio and Natalie Portman, it may likely be successful. Yet, the argument given completely ignores any film production details, which can determine success. The argument also ignores its intended audience. It can be assumed these toys are popular with children, but how often do children make decisions to go to movies? Also, will these movies be appropriate for kids? These factors need to be considered. Fourth paragraph The argument is based on emotional, not rational appeals, which makes it even more illogical. It does state that these toys are extremely popular; however, how long have they been popular? Most toys are only popular for a short period of time. The most popular toys are always the hottest, latest, must-have item, and toy manufacturers know that. So, they aggressively try to squeeze every dollar they can out of them before the fad is over, and the Hollywood studio is trying to ride this fad while its hot but it wont be hot for long, and they are letting their emotions impact sound business decisions. Fifth paragraph Now, just wrap it all up. Make a conclusion statement that this argument is illogical because it makes false assumptions, ignores critical factors, and bases decisions on emotional appeals.

Top 7 Geometry Apps To Make Math Easier For Students

Top 7 Geometry Apps To Make Math Easier For Students Certain subjects like geometry and algebra are very different from what students are usually used to. This makes it all the more difficult for them to understand it. The fear of having to learn something new and of course the fact that it doesn’t conform to the usual style of learning they are used. Both of these contribute to poor performance in the subject. Geometry is one such subject that students find way too difficult to handle. It is introduced at the very beginning and it only gets progressively worse. Here are a few top apps that are designed to help students learn the subject with ease and these are popularly recommended by even online geometry tutors. App1: GeoCon HD This is a game designed for the iPad and helps students grasp the nuances of planar geometry with ease. This game enables learning by building and touching and is very effective for tactile/kinesthetic learners. Read To Know Top 13 #iPad #Educational #Apps For Kids http://t.co/c6NhHOQilv pic.twitter.com/OW3DcOg9Kq â€" Tutor Pace (@TutorPace) October 7, 2015 App2: Symmetry School Learning Geometry This award winning app is excellent for learning geometry and parents and teachers. They use it alike to teach geometry to kids. Charged at a minimal $3.99, it is an excellent buy and provides great value for money. Value in terms of learning and making the subject interesting and fun enough for kids to learn. App 3: Dragon Shapes â€" Lumio Geometry Challenge This app is perfectly designed to cater to the learning needs of today’s children. Solving math puzzles related to shapes and geometry. This let students unlock Dragon shapes and this game is very popular amongst the student fraternity. And this has up to four academic levels of difficulty. 12 study #apps that lead to #students’ stress free #education https://t.co/6WlETMms1A via @examinercom share via @TutorPace â€" Tutor Pace (@TutorPace) November 23, 2015 App 4: My Geometric Universe This is perhaps the most interesting of apps designed to teach geometry to kids. The player can actually draw shapes using pencils, protractor and set squares and cut them out to use in real world object building! Could you think of a better way to teach geometry and its applications to children? Not surprisingly, this app is very popularly used as geometry homework help by many parents. App 5: Montessori Geometry This app again has a five star rating on many popular review sites and is one of the most comprehensive apps. Best for learning geometry in a fun filled manner. In fact, this app is the popular choice for most editors. For those who label it as a comprehensive, in depth and well crafted one to teach geometry effectively. App 6: Dragon Box Elements This game enables students to learn geometry without them even knowing it! With a variety of puzzles, adventures and problems for them to solve that are built in to the game; they end up learning the subject in a matter of hours (at least the fundamentals)! App 7: Cyberchase 3D Builder If your child is a fan of Cyberchase, all you need to do is download the app and they will start working with it right away! This is a 3D game wherein two of the popular characters Buzz and Delete accidentally delete houses and the player has to help them build 3D shapes from 2D ones. Innovatively designed, this app helps students visualize and build shapes in 3 dimensions and this is very helpful in learning geometry and serves as the best geometry assignment help for math. Top 10 #Mobile #Apps For #College Students In 2015 https://t.co/AI6cPqjJhN via @TutorPace â€" Tutor Pace (@TutorPace) November 23, 2015 Summary Today’s education standards are very high and investing in apps that help students understand the fundamental concepts better and use them effectively are essential for them to be able to master the subject. This is specifically true when it comes to maths. The above mentioned apps are sure to be of help when it comes to mastering math and acing their exams.

My Child is Having Homework Problems, How Can Online Tutor Help

My Child is Having Homework Problems, How Can Online Tutor Help 0SHARESShare Often children get stuck up doing their day to day homework problems. The reason can be lack of understanding while learning the topic at school or lack of time to complete the homework after the school hours. Whatever may be the reason, but children requires some extra help to fill up their gaps in understanding the topics, guide them in solving difficult homework problems or revise the lessons for test prep. There are a number of websites offering  online tutoring  services offer tutors and resources to facilitate an easy and convenient method of working.   The tutoring websites provide online help to the children to complete their school homework done at the time they want. The homework is done by the children and not by the tutor. Often people criticize the concept of homework as an extra burden to the children. Although, in reality, homework help children in improving their skills and abilities by revising the topics learnt in the school classroom.   Online tutors work very close with the students to work on their homework like reading and understanding the topic, to memorize, problem solving, preparing QA, designing projects and working on experiments. They help improving memory and thought process. The daily practice work and revision of school work prepare your child get ready for the next day. They prepare students for difficult topics with extensive knowledge.   Online tutors not only teach the subject conceptually but make them learn how to learn the topics. They make student self-learner, disciplined and responsible. The teaching methodology, Math problem solving techniques and practical approach towards learning Science is excellent with online tutoring. [starbox id=admin]

Online Antiderivative Tutors

Online Antiderivative Tutors Derivatives and anti-derivatives are the two important methods used to solve questions in Calculus. Anti-derivative is the process of finding the area covered below the graph of the given function. Anti-derivative is the opposite of the derivative process and is commonly known as the process of Integration. Example 1: Find the anti-derivative of the function, f(x) = x3- 2x In order to find the anti-derivative of the above function, we can use the formula The Power Rule of Integration says that (x) n dx = x (n+1)/ (n+1) + c where c is a constant Using the above formula we get, f(x) dx = x3+1/ (3+1) - 2x1+1/ (1+1)+ c f(x) dx = x4/ 4 - 2 x2/ (2)+ c f(x) dx = x4/4 x2 + c Example 2: Find the anti-derivative of the function, f(x) = 5x4 + 4x3 x-2 In order to find the anti-derivative of the above function, we can use the formula: The Power Rule of Integration says that (x) n dx = x (n+1)/ (n+1) + c where c is a constant Using the above formula we get, f(x) dx = 5 * x4+1/ (4 +1) + 4 * x3+1/ (3 +1) x-2+1/ (-2+1) + c f(x) dx = 5 * x5/ 5 + 4 * x4/ (4) x-1/(-1) + c f(x) dx = x5 + x4 + 1/x + c

GMAT Combinatorics 1.2 Problem Solutions

GMAT Combinatorics 1.2 Problem Solutions GMAT MBA Admissions Blog 1. Suppose you perform the following experiment - You flip a coin 5 times and record the results. How many different outcomes are there? (A result being a 5-character long string of H's and T's, such as HHTHT) Solution: For every flip of the coin, there are two possible outcomes. Because we flip the coin 5 times, according to the fundamental principle of counting the number of possible outcomes is: [latex]2 imes 2 imes 2 imes 2 imes 2 = 32[/latex] Note that this calculation can also be expressed by [latex] 2^5 [/latex]. In fact, if you flip a coin [latex] n [/latex] times, the number of possible outcomes is [latex] 2^n [/latex]. __________ 2.0 You receive a new debit card in the mail and you are asked to create a new PIN (Personal Identification Number) for your debit card. The PIN must be 4 digits long and each digit must be one of the numbers 0 - 9. You can use the same digit more than once. How many possible PIN numbers are there? Solution: Each number in your PIN can be one of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. One digit must be assigned on each of four places. So, by the fundamental counting principle, the number of outcomes is: [latex]10 imes 10 imes 10 imes 10 = 10,000 [/latex] __________ 2.1 Same as 2, but now you can use each digit only once. Solution: Now that we cannot reuse digits, once we assign a digit to the first place, we will only have 9 options for the second place, then 8 options for the 3rd place and so on. As I mentioned before, this is a permutation - the ordering or a subset of elements taken from a larger set. But, as you'll see in the course of these posts on combinatorics, all the technical jargon and formulas you get in other prep material just reduces to a single principle - the fundamental principle of counting. The number of possible PIN numbers is now, [latex] 10 imes 9 imes 8 imes 7 imes [/latex] = 5040 __________ 2.2 Same as 2, but now you can use each digit only once and you cannot begin the PIN with a zero. Solution: This is very similar to the last problem with one exception. We only have nine possibilities for the first digit. So the number of possible PIN numbers is [latex]9 imes 9 imes 8 imes 7 = 4536 [/latex] __________ 3. Sam, Sally, Xanthar, and their parents drive to the park in their Prion (a Prius that has been modified by Xanthar for hydrogen ion technology). If the front of the car has two seats (the drivers seat and the passenger seat), the back seat will hold three people, and the two parents sit in the front and Sam, Sally, and Xanthar sit in the back seat, how many ways can the family be arranged in the car if each seat contains only one passenger. Solution: The total arrangements in the car depends on the arrangements of two groups - the kids and the parents. We will take the product of these two arrangements because they are not mutually exclusive. [latex]Kid Arrangements = 3 imes 2 imes 1 = 6[/latex] [latex]Parent Arrangements = 2 imes 1 = 2[/latex] [latex] Total Arrangements = 6 imes 2 = 12[/latex] __________ 4.0 You roll two die. How many possible outcomes are there? Solution: You can think of the outcome of one roll as an ordered pair or numbers [latex](x, y)[/latex]. For instance, the ways to roll a sum of seven are [latex](1, 6), (2, 5), (3, 4), (4, 3), (5, 2),[/latex] and [latex](6, 1)[/latex]. Obviously, there are six options for the first number in the ordered pair, and six options for the second number in the ordered pair. So, according to the fundamental principle of counting the number of outcomes is: [latex]6 imes 6 = 36[/latex] __________ 4.1 Same as 4.0. How many ways can you get two even numbers? Solution: We can use the same thinking as before. However, this time, because we are only considering even numbers, there are only 3 options for each number. Thus, the number of possibilities is [latex]3 imes 3 = 9[/latex] __________ 4.2 Same as 4.0. How many ways can you get two odd numbers? Solution: This is the exact same problem as the one above. See the solution to 4.1. __________ 4.3 Same as 4.0. How many ways can you get one even and one odd number? Solution: This may seem somewhat complicated as we don't know in what order the even number and odd number appear in our ordered pair. However, if you were paying attention when you read my original combinatorics post, you might be thinking about the 'complement method.' In fact, it's perfect for this problem. On any given roll, one of three things will happen: You'll get two odds You'll get two evens You'll get an even and an odd We already know the number of ways in which the first two outcomes can happen, and we know the total number of outcomes. So, we can use the complement method: Even Odd = Total - Two Odds - Two Evens Even Odd = 36 - 9 - 9 = 18 __________ 4.4 Same as 4.0. Now take the sum of the two upward facing numbers. How many ways can the sum be an even number? Solution: We can only get and even sum in two ways: Even + Even = Even Odd + Odd = Even Using the problems we already solved above, we know that there are nine ways to roll two evens and nine ways to roll two odds. Since these are mutually exclusive events we add to get the total number of outcomes, which is 18. __________ 4.5 Same as 4.0. Now take the product of the two upward facing numbers. How many ways can the product be an even number? Solution: We proceed as above. We get an even product in one of two ways Even X Even = Even Even X Odd = Odd X Even = Even The number of ways the first even can happen is nine and the number of ways the second event can happen is 18. Since they are mutually exclusive, we add, and get 27. 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Distracted How to Develop a Focused Study Plan

Distracted How to Develop a Focused Study Plan Improving Academic Performance So you want to learn how to study better and use your time wisely and effectively? You’ve got your books, pen, paper, computer, and mind to dig in for a solid chunk of time and maximize your study period? Well, think of it like exercise. Have you ever gone for a run? The first ten to fifteen minutes can be a real pain, can’t they? But once you get into the rhythm of it and your lungs and muscles are warmed up, it starts to flow. It starts to feel great. It even starts to be fun! And the payoffs are numerous. Below are some excellent tips for most effectively utilizing your study period while also taking care of your stress levels and well-being. Minimize Distractions First things first, folks. You’ve got to put the phone away. You know this. How can we really focus if we are distracted with reading texts, scrolling Instagram, and sending funny Snaps to our friends? Think of it like taking an hour to go for a jog or choosing a side salad instead of french fries once in a while - we make sacrifices because they are ultimately good for us and help us feel better. So know that when you go into a study period, whether it’s twenty minutes or ninety, that you are going to turn the phone off (or leave it downstairs), and view checking it when you’re finished as a nice little reward. (More on rewards in a bit.) If you need technology to study, I recommend using a laptop and disengaging text and email dings and logging off Facebook and other social media sites. The best of both worlds is to be able to have the temptation of technological distraction but not giving in! This really builds up strength in the brain. Make a time-management plan and reward yourself Focus on time-management. If you are a truly squirmy individual who can barely study for half an hour, I recommend breaking your study chunk into three or four segments - you can set a timer if you like, and every fifteen or twenty minutes take a stretch or drink some water or give yourself two minutes to goof off. And those rewards are essential. Yes, we are sophisticated human beings, but we are also animals, and much like Pavlov’s dogs we can train ourselves pretty quickly - in this case with rewards and self-soothing. Let’s say you put in a solid thirty minutes reviewing ACT questions or AP Composition rules. When that timer dings and you take a stretch, give yourself a reward that you find soothing and nurturing. It might be a little snack or warm drink, or perhaps a promise to yourself that you’ll get a massage or a do a relaxing meditation or buy that shirt you’ve been eyeing. I recommend small rewards for increments like twenty, thirty, and forty minutes and larger re wards when you’ve completed a practice test, essay, or done well on an exam. Know yourself Developmental psychologist Howard Gardner discovered and nurtured the idea of multiple intelligences and how most individuals tend to perform at a higher level in two or three categories (i.e. verbal, visual, logical, etc.), and a bit lower in one or two. This is, of course, not fool proof or set in stone, but it might help give you a better understanding of your natural strengths and areas where you can grow. (To learn more, click here.) Bottom line? Know yourself as a student. Know your strength as a studier. Do you benefit from flash cards? Online programs like Quizlet? Do you study better alone or with a partner? Does it help to talk out loud? Are you more of a verbal or visual person? All of these factors are important when it comes to studying and essential when it comes to overall learning. I am usually someone who works better alone, but I found in college that when I studied for larger exams with a partner from a class (not a close friend with whom I would just end up gabbing) I was more successful. The motivation and accountability of a study partner was a positive factor for me. I also knew that taking notes and using tools like flash cards were beneficial for me, whereas viewing clips and videos didn’t support my memorization process as much. You might find that forty minutes of studying each night is the sweet spot for you, or perhaps you have one of those very focused minds and can pull off a solid ninety minutes to two hours before needing a break. Maybe you prefer standing to sitting. Music to silence. Libraries to your desk at home. See what works for you and nurture that. Warm up to the tricky material Attempt at times to go for the jugular. It’s easy to focus when we study on the areas we like or know really well, but this can end up being a waste of time. Be willing to get uncomfortable and study the trickier concepts and shakier methods. Practice those. Then do it again. If, however, a concept is really stumping you or you are growing inconsolably frustrated, move on. Make a note that you’ll talk to the teacher or a classmate and gain more insight and clarity to what is confusing you. Don’t get discouraged - we all get overwhelmed and confused! (Here’s a great TED talk on growth mindset, which can often help motivate and inspire us when we are feeling stuck.) Take care of yourself! Most of all, take care of yourself. Don’t study when you are exhausted, hungry, or angry - studying will only make you feel worse, and you likely won’t retain the information as well. Make sure to get plenty of rest and drink lots of water, and study when you’ve had a snack and are in a relatively balanced mood. And cramming is so nineties, so don’t do it! Always keep a good balanced perspective and work on that growth mindset, and nothing can stop you from growing and succeeding as a student! Questions or comments? We would love to hear from you! Contact us here. About the Author Stephanie Ingraham is a former English teacher turned writer and tutor with a BA in English from UCLA and a Masters in Education from Pepperdine University in Los Angeles. She is deeply passionate about education, psychology, child and adolescent development, literature, and writing. She believes the education world can benefit greatly from the meditation world - mindfulness and self-compassion are key! In her free time she loves reading and writing, music, baking, yoga, dance, animals, and exploring new cities. She currently lives in Chicago, Illinois.