Mathematics at University

High school mathematics classes are very different than those at university. Yes, mathematics classes at university are more difficult, but it is more than just that. When you learn mathematics at high school, all of the classes are about solving problems. The students are presented with the theory, the teacher demonstrates how to solve the problem using the theory and then the students try it for themselves.

What happens at university? Firstly, the classes are now lectures and so mathematics is now presented to the student rather than co-created with the student. Some problems are demonstrated, but often the lecture is mostly theory. The drawback is that the student must choose to put in the time in doing the problems outside of the class.

Some universities provide one hour of tutorial time per week or per two weeks. In these tutorials, often a postgraduate at the university will help the students in solving problems from a problem set. While this is welcomed, often the postgraduate is not as approachable as a high school teacher. The same can be said about the lecturer. Yes, you will find some lecturers who are only too happy to offer one-to-one time helping the students but this is not the norm. Most lecturers have their time taken up by research and they view classes as a secondary role of their job. This, of course, is not true for all third level institutes.

In addition to this, the mathematics courses themselves vary. For example, a student taking a course in statistics would be solving many more problems than a student taking pure algebra. Most questions in pure algebra are not “problem based” but rather “proof based”. That is, in statistical classes the student will need to solve a problem and in pure mathematical classes students would mostly be proving a result. The former is more reminiscent of high school mathematics classes.

My advice for students entering a mathematics course at a university would be to stay on top of the questions or problems the lecturer assigns. You will not have the same time in class you would have had at high school for solving problems. Mathematics is not a spectator sport; you must work at it. Mathematics is presented to students as something to “watch” but it is something to work at. And of course, if you find yourself having trouble in your course, then seek help straight away!


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Board Examination Study Tips

It is that time of year when feverish preparations begin – the Examination Fever. Many young students are getting ready for the biggest test of their academic lives, one that will determine their choice of career and how their futures will shape up. The 10th standard examinations or Board Examinations follow many patterns according to the syllabi and the academic councils the schools are affiliated to. Getting high marks and percentages overall in all subjects is key to enhancing chances of a good education in a reputed institution; therefore students should take extra steps in equipping themselves well in the preparations for exam study.Students at this level have six to seven subjects with allocation of marks and grades combined for a subject grouping. Mathematics and Science take predominance over other subjects like Social Studies, English or Other Languages. This is because for most technical courses post school and getting admitted into college depend on excellent percentages in these two subjects. While subjects like English depend on the student’s excellent uptake of grammar and presentation of answers in a neat format with the relevant points concisely written, Mathematics and Science depend largely on accuracy in answers and results.Some examination tips for High School• By understanding the format of exams corresponding to the syllabus undertaken, a student can work out a study schedule depending on subjects that need more attention and time. Having a timetable based subject-wise and topic-wise will greatly benefit your study schedule; always remember to complete the schedule as per the timetable you have prepared• Referring to previous question paper samples and guides helps obtain an insight into the kind of questions that can be expected and prepare a mental plan on how to answer the questions• Resorting to malpractices or depending entirely on memorizing content can be disastrous. In case of exam panic or a wrong move, the mind goes into a freeze making thinking and recollection difficult. It is better to understand content, rephrase questions on how best to bring out the answers and keep doing the tasks over and over to perfect the method and analyze and correct mistakes, especially in problem solving• One of the best ways to retain content the student has read is to write down points or make brief notes that will help to remember key points to prepare the flow of content• When in doubt, seek help. Parents, teachers, friends, guides are always around to help clear doubts. Published guides help but where they fail is the kind of one on one interaction that you can have with peers and superiors• Learn to practice time management which is very essential in answering question papers. Practicing writing speeds can help improve answering skills when time is of utmost importanceBesides these academic tips, there are several other areas that the student has to keep in mind when preparing for Board exams.i. Choose a study area without distractions and ambient noises from traffic, TV screens, computers and other gadgets that can be a disturbance or intrusion. Conversations with friends can be restricted to times when you take a break from studyingii. Getting proper nutrition, exercise and sleep recharges the body and fills it with energy resources which are very essential. Skipping meals and sleeping less will tire the body and mind and leave you exhausted by the time examinations arriveiii. Avoid places and situations that can cause anger and negative emotions to surface. The unnecessary anxiety and worry will not help in any wayiv. Always take constant breaks from study to re-energize the mind and body. Cramming the brain with too much information or too many facts in a short span of time is not a good idea. Take time off to indulge in a favorite hobby like listening to music, painting or photography; going for a short walk and meeting friends for a cup of coffee is a good idea provided this does not cut into your daily study schedule and you are able to get back into study mode again
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Alternative Financing Vs. Venture Capital: Which Option Is Best for Boosting Working Capital?

There are several potential financing options available to cash-strapped businesses that need a healthy dose of working capital. A bank loan or line of credit is often the first option that owners think of – and for businesses that qualify, this may be the best option.

In today’s uncertain business, economic and regulatory environment, qualifying for a bank loan can be difficult – especially for start-up companies and those that have experienced any type of financial difficulty. Sometimes, owners of businesses that don’t qualify for a bank loan decide that seeking venture capital or bringing on equity investors are other viable options.

But are they really? While there are some potential benefits to bringing venture capital and so-called “angel” investors into your business, there are drawbacks as well. Unfortunately, owners sometimes don’t think about these drawbacks until the ink has dried on a contract with a venture capitalist or angel investor – and it’s too late to back out of the deal.

Different Types of Financing

One problem with bringing in equity investors to help provide a working capital boost is that working capital and equity are really two different types of financing.

Working capital – or the money that is used to pay business expenses incurred during the time lag until cash from sales (or accounts receivable) is collected – is short-term in nature, so it should be financed via a short-term financing tool. Equity, however, should generally be used to finance rapid growth, business expansion, acquisitions or the purchase of long-term assets, which are defined as assets that are repaid over more than one 12-month business cycle.

But the biggest drawback to bringing equity investors into your business is a potential loss of control. When you sell equity (or shares) in your business to venture capitalists or angels, you are giving up a percentage of ownership in your business, and you may be doing so at an inopportune time. With this dilution of ownership most often comes a loss of control over some or all of the most important business decisions that must be made.

Sometimes, owners are enticed to sell equity by the fact that there is little (if any) out-of-pocket expense. Unlike debt financing, you don’t usually pay interest with equity financing. The equity investor gains its return via the ownership stake gained in your business. But the long-term “cost” of selling equity is always much higher than the short-term cost of debt, in terms of both actual cash cost as well as soft costs like the loss of control and stewardship of your company and the potential future value of the ownership shares that are sold.

Alternative Financing Solutions

But what if your business needs working capital and you don’t qualify for a bank loan or line of credit? Alternative financing solutions are often appropriate for injecting working capital into businesses in this situation. Three of the most common types of alternative financing used by such businesses are:

1. Full-Service Factoring – Businesses sell outstanding accounts receivable on an ongoing basis to a commercial finance (or factoring) company at a discount. The factoring company then manages the receivable until it is paid. Factoring is a well-established and accepted method of temporary alternative finance that is especially well-suited for rapidly growing companies and those with customer concentrations.

2. Accounts Receivable (A/R) Financing – A/R financing is an ideal solution for companies that are not yet bankable but have a stable financial condition and a more diverse customer base. Here, the business provides details on all accounts receivable and pledges those assets as collateral. The proceeds of those receivables are sent to a lockbox while the finance company calculates a borrowing base to determine the amount the company can borrow. When the borrower needs money, it makes an advance request and the finance company advances money using a percentage of the accounts receivable.

3. Asset-Based Lending (ABL) – This is a credit facility secured by all of a company’s assets, which may include A/R, equipment and inventory. Unlike with factoring, the business continues to manage and collect its own receivables and submits collateral reports on an ongoing basis to the finance company, which will review and periodically audit the reports.

In addition to providing working capital and enabling owners to maintain business control, alternative financing may provide other benefits as well:

It’s easy to determine the exact cost of financing and obtain an increase.
Professional collateral management can be included depending on the facility type and the lender.
Real-time, online interactive reporting is often available.
It may provide the business with access to more capital.
It’s flexible – financing ebbs and flows with the business’ needs.
It’s important to note that there are some circumstances in which equity is a viable and attractive financing solution. This is especially true in cases of business expansion and acquisition and new product launches – these are capital needs that are not generally well suited to debt financing. However, equity is not usually the appropriate financing solution to solve a working capital problem or help plug a cash-flow gap.

A Precious Commodity

Remember that business equity is a precious commodity that should only be considered under the right circumstances and at the right time. When equity financing is sought, ideally this should be done at a time when the company has good growth prospects and a significant cash need for this growth. Ideally, majority ownership (and thus, absolute control) should remain with the company founder(s).

Alternative financing solutions like factoring, A/R financing and ABL can provide the working capital boost many cash-strapped businesses that don’t qualify for bank financing need – without diluting ownership and possibly giving up business control at an inopportune time for the owner. If and when these companies become bankable later, it’s often an easy transition to a traditional bank line of credit. Your banker may be able to refer you to a commercial finance company that can offer the right type of alternative financing solution for your particular situation.

Taking the time to understand all the different financing options available to your business, and the pros and cons of each, is the best way to make sure you choose the best option for your business. The use of alternative financing can help your company grow without diluting your ownership. After all, it’s your business – shouldn’t you keep as much of it as possible?