Many universities and colleges allow students to use advanced graphical calculators for exams in math courses, including linear algebra, calculus and engineering. Having the appropriate calculator can prove to be a huge advantage in terms of getting the correct answer and saving time. Even if the handwritten manual working is required, a good calculator can help to check the correctness of the answer.
Best Calculator for Linear Algebra
The key calculations in linear algebra include calculating the inverse and determinant of matrices. Additional features that are useful in calculators include the ability to calculate eigenvalues, eigenvectors, and RREF (reduced row echelon form). These features can be great time savers (or at the minimum, useful tools for checking your answer), as matrix operations are often tedious and prone to human error.
This calculator is good enough up till senior undergraduate level or even graduate level, for computational intensive modules, such as computational physics or any module that requires linear algebra calculations.
Often, linear algebra courses include applications to differential equations as well, which overlaps with the next topic on Calculus.
Update: For the latest TI-85/86 models, there is a new “Matrix Mode” inbuilt into the calculator that can perform basic matrix operations (including inverse) and other advanced operations such as LU Decompositions, and finding eigenvalues/eigenvectors.
Note that paradoxically, the newer TI calculator models may be cheaper than the older ones.
For Calculus, the important features that a calculator should have are the ability to perform numerical differentiation and integration. There are also some amazing apps for TI83/84 that can perform symbolic differentiation, that is, find the derivative of a function in symbols (not just the numerical value at certain values of x).
In my experience as a student and educator, TI (Texas Instruments) calculators dominate the market and are generally considered a good choice. But there are other viable alternatives that can also be considered good for linear algebra, calculus or engineering math.
The Casio fx-9750 (and related series) calculator is able to calculate determinant of matrix as well as basic matrix operations such as multiplying matrices, finding the inverse of matrix, etc.
As mentioned above, the main advantage of Casio graphical calculators is their low price. For advanced features, the TI calculators definitely trump over the Casio calculators.
Another alternative to TI calculators are the HP graphical calculators. Let us check out the most powerful HP calculator, the HP 50g Graphing Calculator.
The HP 50g Graphing Calculator has a “MatrixWriter form” to facilitate the entry of matrices. It is essentially like an Excel spreadsheet. Once the matrix is entered, there is a myriad of functions that can be applied, such as finding the determinant, trace, transpose, and rank of a matrix.
Calculate the Taylor/Maclaurin series of a function symbolically (up to 4-th order relative power, i.e., the difference between the highest and lowest power in the expansion is 4)
Partial Derivatives (Multivariate Calculus)
Multiple Integrals such as double integral
Vector Calculus such as del, gradient, divergence, curl
Differential Equations
Fourier series
The list above is quite impressive! Overall, the HP 50g Graphical Calculator is a very strong competitor to the TI series graphical calculators.
Best Calculator for Engineering
Engineers often need to use Linear Algebra, as well as Calculus. Hence, the best calculator for engineering often overlaps with the best calculator for linear algebra or calculus. Do check out our above reviews and pick the calculator that best suits your needs.
America (and prosperous European countries like UK and France), being 1st world countries, are sometimes concerned about “First World Problems” that most other countries do not have time/energy/money to care about.
Two health concerns that are very popular in America, but virtually unknown in most Southeast Asian countries are:
Vaccines Health Concerns
Although the main research linking MMR Vaccines to Autism has been retracted, many Americans, including President Donald Trump, have expressed their concern about vaccines. There are many anecdotal stories from parents whose children are doing well developmentally, until the day they took the vaccine where strange effects happened, including autistic regression.
Read here about a Nature article on “The real issues in vaccine safety”. By the way, Nature is the top science journal in the world, it is considered a tremendous achievement for any professor to publish in Nature.
The main author behind the MMR-Autism link, Andrew Wakefield, has published his version of the story in his book called “Callous Disregard”. He has been called a fraud, but yet many people do believe in his theory. Notably, in his retracted paper Wakefield did not claim that vaccines cause autism, he just investigated the link and basically said that more research needs to be done. His punishment was very severe (lost his UK doctor’s licence; he spent a decade earning his Gastroenterologist specialist degree), and some people believe it to be a conspiracy theory backed by the billion-dollar vaccine pharmaceutical giants.
“We have identified a chronic enterocolitis in children that may be related to neuropsychiatric dysfunction. In most cases, onset of symptoms was after measles, mumps, and rubella immunisation. Further investigations are needed to examine this syndrome and its possible relation to this vaccine.” (Andrew Wakefield’s paper’s final conclusion.)
Basically, vaccinations rely on a phenomenon called “herd immunity”, it requires at least 90-95% of the population to be vaccinated in order for it to be successful. Hence, many people dropping out of the vaccinations can cause the “herd immunity” to be lost, which may be dangerous. On the other hand, vaccines contain dangerous ingredients like preservatives and viruses, and even used to contain a mercury compound called thimerosal, which no doubt is something unnatural that you wouldn’t want to put in your body. Due to the vaccine controversy, thimerosal has now been discontinued in most vaccines.
In Southeast Asia, I would say that more than 90% of people do not know what gluten is (though they eat it everyday). In Laymen’s terms, it is a type of protein that is found in wheat, barley, rye, etc. In America, many people have been tested to have gluten sensitivity, causing digestive problems such as Crohn’s disease or Celiac disease. Again, similar to vaccines, most people have no problem at all eating gluten, but in a selected minority of the population, it can cause severe problems.
The digestive system is said to be a “second brain”, (see The Strange Location of Your Second Brain). It contains a lot of neurotransmitters. Hence, many scientists have started to notice the gut-brain connection. Read this Harvard article that links anxiety and depression to digestive (gut) problems. Hence, for people with gluten sensitivity or allergy, gluten can be the starting trigger for their other problems like depression/anxiety. It has also been linked to ADHD and even schizophrenia.
Check out this book (1,001 positive reviews) on the connection between the gut (digestive system) and the brain:
It turns out that US students aren’t that bad at math, they just have no motivation to do the PISA test properly. (The PISA test is an external test that has no bearing on their school academic results.)
It’s no secret that young Americans perform poorly on math and science tests, especially compared to their peers in countries like Singapore, Korea and China, where math scores are among the highest in the world. Now, a working paper surfaces a fundamental reason for that weak performance: American students are simply not trying hard enough.
In the latest results of the Programme for International Student Assessment (PISA), US students ranked roughly average among the 75 participating countries. The PISA tests, administered by the OECD every three years, assess 15-year-olds around the world on math, science and reading. Governments and policy makers point to the outcomes when making the case for education reform.
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The researchers also ran a simulation, and found that if the 15-year-olds in the US had been given the same cash bonus in 2012 when taking the assessment, America would have ranked 19th in the PISA math test instead of 36th among 65 nations.
This is very bad news. Graduate students are already poor (stipend is already low to begin with and fixed for the duration of study). A very bad policy for grad students.
The tax overhaul passed Thursday by House Republicans could cost graduate students thousands of dollars, prompting a backlash from students and university leaders who say the proposal could make graduate degrees unaffordable, especially for low-income students.
A provision tucked away in the House’s bill would count the tuition discounts given to many grad students as income, meaning that students would pay taxes on tens of thousands of dollars that they never see. The bill would double or even triple many students’ taxes.
A survey from the Princeton Election Consortium has found that Hillary Clinton has a 99 per cent chance of winning the election over Donald Trump.
Three days before the election, Ms Clinton has a projected 312 electoral votes, compared to 226 for Mr Trump. A total of 270 electoral votes are needed to win.
The probability statistic was found by the university’s statistical Bayesian model.
The developer of the model, neuro and data scientist Princeton professor Sam Wang, correctly predicted 49 out of 50 states in 2012.
“I have to say a lot of people have been asking this question. No, really. A lot of people come up to me and they ask me. They say, ‘What’s 2+2’? And I tell them look, we know what 2+2 is. We’ve had almost eight years of the worst kind of math you can imagine. Oh my God, I can’t believe it. Addition and subtraction of the 1s the 2s and the 3s. It’s terrible. It’s just terrible. Look, if you want to know what 2+2 is, do you want to know what 2+2 is? I’ll tell you. First of all the number 2, by the way, I love the number 2. It’s probably my favorite number, no it is my favorite number. You know what, it’s probably more like the number two but with a lot of zeros behind it. A lot. If I’m being honest, I mean, if I’m being honest. I like a lot of zeros. Except for Marco Rubio, now he’s a zero that I don’t like. Though, I probably shouldn’t say that. He’s a nice guy but he’s like, ‘10101000101,’ on and on, like that. He’s like a computer! You know what I mean? He’s like a computer. I don’t know. I mean, you know. So, we have all these numbers, and we can add them and subtract them and add them. TIMES them even. Did you know that? We can times them OR divide them, they don’t tell you that, and I’ll tell you, no one is better at the order of operations than me. You wouldn’t believe it. So, we’re gonna be the best on 2+2, believe me.”
which is essentially the black and white version of the TI-84 Plus CE Color.
which still supports the linear algebra apps.
is a good suggested calculator for Calculus modules.
. CAS stands for “computer algebra system”, which means that the calculator is capable of producing symbolic results rather than just numerical results.
. An immediate advantage of Casio calculators is their low price.
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Singapore Maths Tuition 