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Topics - Masuma Parvin

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1
Interesting Maths / Number Puzzles
« on: July 07, 2018, 01:40:20 PM »


By using your numerical and logical reasoning skills please try to figure out which number is missing in the questions below. The numbers around will give you the clues you need to solve the puzzle.

2
Interesting Maths / Amazing Wizard Tricks You Can Do With Basic Math
« on: April 17, 2017, 12:18:38 PM »
Here are a few easy but impressive tricks that you can use to intimidate your friends and amaze your enemies.

1.Perfectly Sort Coins Without Looking at Them:
The Magic is :

Let's start with a trick a moron could do. Let's say we're using a handful of coins. First you close your eyes (or get blindfolded) and tell your spectators to shake up the coins and throw them on the table. All you need is one piece of information: how many of the coins are facing heads-up.Then, without ever peeking at the coins, you sort them into two piles, blindly flipping and shuffling them as if your hands were being guided by the spirit world. You magically wind up with the exact same number of heads in each pile. Every time.

The Math:

Let's say your spectators tell you that there are six heads-up coins in the pile. All you need to do is grab that number of coins and flip them. Just any six random coins. Take the ones you flipped and move them to their own pile, which we'll call Pile #1. The remaining coins are Pile #2. Both piles will contain the same number of heads.


3
Public Health / Is Coffee *Really* Bad for You?
« on: April 10, 2017, 11:56:01 AM »
Regularly drinking coffee may help you live longer. It may prevent Parkinson's disease, depression, and type 2 diabetes, plus promote a healthy heart and liver.Coffee can help lower the risk of stroke and potentially coronary heart disease at 2 to 3 cups a day, but it can also raise unhealthy LDL cholesterol depending on how it's brewed.
So How Much Caffeine Is Healthy?
The amount of caffeinated coffee you need to drink for health benefits might depend on your genes. You could be a "fast caffeine metabolizer," meaning your body breaks it down quickly. Fast metabolizers may have heart health benefits from drinking between 2 and 4 cups a day. Slow caffeine metabolizers tend to do better with less. How do you know which type you are? See a registered dietitian who offers a nutrigenomics test to find out.Some people are especially caffeine-sensitive and might need to cut down even more. If you feel anxious or have trouble sleeping, it may be worth replacing some of your caffeinated brew with decaf and slowly weaning yourself down.

4
Public Health / 7 Natural Ways to Add More Zinc to Your Diet
« on: April 10, 2017, 11:34:53 AM »
I have read from a magazine the importance of zinc in our diet and want to share it with everyone .Zinc is a powerful micronutrient that's essential for immunity, cell growth and division, wound healing, and immune function. One recent study found that even a slight deficiency in zinc can affect your digestion. The recommended dietary allowance (RDA) of zinc is 8mg/day for women (11mg/day for men) and a tolerable upper intake level (UI), which is essentially your maximum amount of any nutrient before it can pose a threat, is 40mg/day. You can get the proper zinc each day by incorporating zinc-boosting superfoods into your diet. But don't try to get zinc by popping a supplement. Non-food zinc supplements can actually be toxic! But rest easy, knowing zinc from food sources is nontoxic!

5
Applied Maths / 6 Everyday Examples of Math in the Real World
« on: April 09, 2017, 01:42:10 PM »
1.Math helps you build things:
Ask any contractor or construction worker and they’ll tell you just how important math is when it comes to building anything. Creating something that will last and add value to your home out of raw materials requires creativity, the right set of tools, and a broad range of mathematics.

Figuring the total amount of bags of concrete needed for a slab, accurately measuring lengths, widths, and angles, and estimating project costs are just a few of the many cases in which math is necessary in real life home improvement projects.

Some students may say they don’t plan on working in construction and this may be true, but many will own a home at some point in their life. Having the ability to do minor home improvements will save a lot of money and headache. Armed with math, they will also have the ability to check the work and project estimates, ensuring they’re getting the best value.
2. Math is in the grocery store
One of the more obvious places to find people using math in everyday life is at your neighborhood grocery store. Grocery shopping requires a broad range of math knowledge from multiplication to estimation and percentages.

Calculating price per unit, weighing produce, figuring percentage discounts, and estimating the final price are all great ways to include the whole family in the shopping experience.

3. Math makes baking fun!
More math can be found in the kitchen than anywhere else in the house. Cooking and baking are sciences all their own and can be some of the most rewarding (and delicious) ways of introducing children to mathematics. After all, recipes are really just mathematical algorithms or self-contained step-by-step sets of operations to be performed. The proof is in the pudding!

Working in the kitchen requires a wide range of mathematical knowledge, including but not limited to:

measuring ingredients to follow a recipe
multiplying / dividing fractions to account for more or less than a single batch
converting a recipe from Celsius to Fahrenheit
converting a recipe from metric (mL) to US standard units (teaspoon, tablespoon, cups)
calculating cooking time per each item and adjusting accordingly
calculating pounds per hour of required cooking time
understanding ratios and proportions, particularly in baking (ex. the recipe calls for 1 egg and 2 cups of flour, then the ratio of eggs to flour is 1:2).

4. Math takes the risk out of travel
Math comes in handy when travelling and shows up in various ways from estimating the amount of fuel you’ll need to planning out a trip based on miles per hour and distance traveled. Calculating fuel usage is crucial to long distance travel. Without it, you may find yourself stranded without gas or on the road for much longer than anticipated. You may also use math throughout the trip by paying for tolls, counting exit numbers, checking tire pressure, etc.

Long before GPS and Google Maps, people used atlases, paper road maps, road signs, or asked for directions in order to navigate throughout the country’s highways and byways. Reading a map is almost a lost art, but requires just a little time, orientation, and some basic math fundamentals. Teaching students how to use their math skills to read maps will make them safer travelers and less dependent on technology.

In order to use any map, you must first orient yourself, meaning to find your current position on the map. This will be point A. The simplest way to do this is to locate the town you’re in then the nearby crossroads, intersection or an easily identifiable point such as a bridge, building, or highway entrance. Once you’ve established a starting point, locate where on you want to go (point B). Now you can determine the best route depending on terrain, speed limit, etc.
5. Math helps you save money
Many experts agree that without strong math skills, people tend to invest, save, or spend money based on their emotions. To add to this dilemma, those individuals with poor math fundamentals typically make greater financial mistakes like underestimating how quickly interest accumulates. A student who thoroughly grasps the concepts of exponential growth and compound interest will be more inclined to better manage debt.

Financial knowledge decays over time, so it’s important to keep young people involved. By continually showing how specific math lessons apply to real life financial situations and budgeting, kids can learn how to properly spend and save their money without fear or frustration.
6. Math lets you manage time
Time is our most valuable asset. Without proper planning, the day can slip through out fingers and our list of duties and responsibilities can start to accumulate. In our fast-paced, modern world, we can easily fall behind and get overwhelmed with all that we have to do. Keeping on schedule has greater weight in our daily lives than ever in history, but it takes more math skills than simply reading a clock or following a calendar to stay on top of everything.

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Nutrition and Food Engineering / আচারি পুঁটি
« on: April 09, 2017, 01:18:06 PM »
আচারি পুঁটি
উপকরণ:
পুঁটি মাছ ২৫০ গ্রাম
শেলী কাসুন্দি ২ চা চামচ
শেলী হলুদগুঁড়ো ১/২ চা চামচ
শেলী লংকাগুঁড়ো ১/২ চা চামচ
কাঁচালংকা ৪ টি
শেলী আচার ২ টেবিল চামচ
সরিষার তেল ৩ চা চামচ
নুন স্বাদমতো
কুমড়ো পাতা ২ টি
প্রণালী:
মাছ কেটে ভালো করে ধুয়ে পরিষ্কার করে নিন। তারপর পরিষ্কার করা মাছে শেলী হলুদগুঁড়ো,শেলী লংকাগুঁড়ো, কাসুন্দি, তেল এবং নুন মাখিয়ে ২ ঘন্টা ম্যারিনেট করে রাখুন। পাতা পরিষ্কার করে ধুয়ে তার ওপর শেলী আচার মাখান এবং ম্যারিনেট করা মাছ রাখুন। মাছের ওপর শেলী আচার দিয়ে আর একটা স্তর করুন এবং বাকি কুমড়ো পাতা দিয়ে ঢেকে দিন। পাতাটা সাবধানে বেঁধে দিন পরিষ্কার সুতির সুতো দিয়ে। চাটুতে প্রতিটি পাশ হালকা করে ভেজে নিন মাছ রান্না হওয়া অবধি। গরম ভাতের সঙ্গে পরিবেশন করুন।

link:http://www.hanglahesel.com

7
History of Mathematics / A brief history of pi
« on: January 13, 2015, 04:55:10 PM »
Everybody knows the value of pi is 3.14…er, something, but how many people know where the ratio came from?

Actually, the ratio came from nature—it’s the ratio between the circumference of a circle and its diameter, and it was always there, just waiting to be discovered. But who discovered it? In honor of Pi Day, here’s a semi-brief history of how pi came to be known as 3.14(1592653589793238462643383279502884197169…and so on).

It's hard to pinpoint who, exactly, first became conscious of the constant ratio between the circumference of a circle and its diameter, though human civilizations seem to have been aware of it as early as 2550 BC.

The Great Pyramid at Giza, which was built between 2550 and 2500 BC, has a perimeter of 1760 cubits and a height of 280 cubits, which gives it a ratio of 1760/280, or approximately 2 times pi. (One cubit is about 18 inches, though it was measured by a person's forearm length and thus varied from one person to another.) Egyptologists believe these proportions were chosen for symbolic reasons, but, of course, we can never be too sure.

The earliest textual evidence of pi dates back to 1900 BC; both the Babylonians and the Egyptians had a rough idea of the value. The Babylonians estimated pi to be about 25/8 (3.125), while the Egyptians estimated it to be about 256/81 (roughly 3.16).


The Ancient Greek mathematician Archimedes of Syracuse (287-212 BC) is largely considered to be the first to calculate an accurate estimation of the value of pi. He accomplished this by finding the areas of two polygons: the polygon that was inscribed inside a circle, and the polygon in which a circle was circumscribed (see figure above, right).

Archimedes didn't calculate the exact value of pi, but rather came up with a very close approximation—he used 96-sided polygons to come up with a value that fell between 3.1408 and 3.14285.

8
History of Mathematics / The History of Phi & The Golden Ratio
« on: January 13, 2015, 04:49:03 PM »
The Golden Ratio – Phi - is known by many other names such as; The Golden Section, Golden Number, Golden Mean, Golden Proportion, Golden Rectangle, Golden Triangle, Golden Spiral, Golden Cut, The Divine Proportion, Fibonacci Sequence, and Tau (τ).
Who first discovered The Golden Ratio?
No one really knows for sure as to who originally discovered the The Golden Ratio – 1.618 - (a.k.a. the Phi ratio) in Human history, but some suggestions point to the ancient Egyptians and even as far back as the ancient Sumerian civilization. However, the ratio was also used by many artists, mathematicians, scientists and philosophers throughout history. The most renowned include the Greeks, such as:

Pythagoras (570–495 BC) was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. He is best known for the Pythagorean theorem which bears his name to this day. Although, because legend and obfuscation cloud his work even more than with the other pre-Socratic philosophers, one can say little with confidence about his teachings, and some have questioned whether he contributed much to mathematics and natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors.
Pythagoras thought that absolute happiness lay in the contemplation of the harmony of the rhythms of the Universe, (“tes teleiotetos arithmon”- the perfection of numbers, the number being both rhythm and proportion). In other words, Pythagoras was looking for a numerical pattern that would explain it all. A goal of Pythagoras’ disciples was to develop a ratio theory. The ratio, a comparison between two sizes represented in mathematics a basic operation of judgment: the perception of the relation between ideas.

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History of Mathematics / Leibniz's Philosophy of Mind
« on: January 13, 2015, 04:37:06 PM »
In a more popular view, Leibniz's place in the history of the philosophy of mind is best secured by his pre-established harmony, that is, roughly, by the thesis that there is no mind-body interaction strictly speaking, but only a non-causal relationship of harmony, parallelism, or correspondence between mind and body. Certainly, the pre-established harmony is important for a proper understanding of Leibniz's philosophy of mind, but there is much more to be considered as well, and even in connection with the pre-established harmony, the more popular view needs to be refined, particularly insofar as it suggests that Leibniz accepts a roughly Cartesian, albeit non-interactionist dualism, which he does not. In fact, Leibniz is justly famous for his critiques, not only of materialism, but also of such a dualism. (Whether Leibniz accepts, throughout his maturity, the idealistic view that all substances are simple unextended substances or monads is an important interpretive issue that has been discussed widely in recent years. We shall not try to resolve the issue here. (See Garber 2009 for comprehensive treatment.) In short, Leibniz made important contributions to a number of classical topics of the philosophy of mind, including materialism, dualism, idealism and mind-body interaction.

But Leibniz has much to say about the philosophy of mind that goes well beyond these traditionally important topics. Perhaps surprisingly, his system sometimes contains ideas of relevance even to contemporary discussions in the cognitive sciences. More generally, he discusses in depth the nature of perception and thought (conscious and unconscious), and of human motivation and striving (or, as he would say, appetition).


1. Matter and Thought
For present purposes, we may think of materialism as the view that everything that exists is material, or physical, with this view closely allied to another, namely, that mental states and processes are either identical to, or realized by, physical states and processes. Leibniz remained opposed to materialism throughout his career, particularly as it figured in the writings of Epicurus and Hobbes. The realms of the mental and the physical, for Leibniz, form two distinct realms—but not in a way conducive to dualism, or the view that there exists both thinking substance, and extended substance. By opposing both materialism and dualism, Leibniz carved himself an interesting place in the history of views concerning the relationship between thought and matter.

Most of Leibniz's arguments against materialism are directly aimed at the thesis that perception and consciousness can be given mechanical (i.e. physical) explanations. His position is that perception and consciousness cannot possibly be explained mechanically, and, hence, could not be physical processes. His most famous argument against the possibility of materialism is found in section 17 of the Monadology (1714):

2. Denial of Mind-Body Interaction, Assertion of Pre-established Harmony
A central philosophical issue of the seventeenth century concerned the apparent causal relations which hold between the mind and the body. In most seventeenth-century settings this issue was discussed within the context of substance dualism, the view that mind and body are different kinds of substance. For Leibniz, this is a particularly interesting issue in that he remained fundamentally opposed to dualism. But although Leibniz held that there is only one type of substance in the world, and thus that mind and body are ultimately composed of the same kind of substance (a version of monism), he also held that mind and body are metaphysically distinct. There are a variety of interpretations of what this metaphysical distinctness consists in for Leibniz, but on any plausible interpretation it is safe to assume (as Leibniz seems to have done) that for any person P, P‘s mind is a distinct substance (a soul) from P‘s body. With this assumption in hand, we may formulate the central issue in the form of a question: how is it that certain mental states and events are coordinated with certain bodily states and events, and vice-versa? There were various attempts to answer this question in Leibniz's time period. For Descartes, the answer was mind-body interactionism: the mind can causally influence the body, and (most commentators have held) vice-versa. For Malebranche, the answer was that neither created minds nor bodies can enter into causal relations because God is the only causally efficient being in the universe. God causes certain bodily states and events on the occasion of certain mental states and events, and vice-versa. Leibniz found Descartes' answer unintelligible (cf. Theodicy, sec. 60), and Malebranche's excessive because miraculous (cf. Letter to Arnauld, 14 July 1686).

Leibniz's account of mind-body causation was in terms of his famous doctrine of the preestablished harmony. According to the latter, (1) no state of a created substance has as a real cause some state of another created substance (i.e. a denial of inter-substantial causality); (2) every non-initial, non-miraculous, state of a created substance has as a real cause some previous state of that very substance (i.e. an affirmation of intra-substantial causality); and (3) each created substance is programmed at creation such that all its natural states and actions are carried out in conformity with all the natural states and actions of every other created substance.

Formulating (1) through (3) in the language of minds and bodies, Leibniz held that no mental state has as a real cause some state of another created mind or body, and no bodily state has as a real cause some state of another created mind or body. Further, every non-initial, non-miraculous, mental state of a substance has as a real cause some previous state of that mind, and every non-initial, non-miraculous, bodily state has as a real cause some previous state of that body. Finally, created minds and bodies are programmed at creation such that all their natural states and actions are carried out in mutual coordination.

3. Language and Mind

Some scholars have suggested that Leibniz should be regarded as one of the first thinkers to envision something like the idea of artificial intelligence (cf. Churchland 1984; Pratt 1987). Whether or not he should be regarded as such, it is clear that Leibniz, like contemporary cognitive scientists, saw an intimate connection between the form and content of language, and the operations of the mind. Indeed, according to his own testimony in the New Essays, he “really believe that languages are the best mirror of the human mind, and that a precise analysis of the signification of words would tell us more than anything else about the operations of the understanding” (bk.III, ch.7, sec.6 (RB, 333)). This view of Leibniz's led him to formulate a plan for a “universal language,” an artificial language composed of symbols, which would stand for concepts or ideas, and logical rules for their valid manipulation. He believed that such a language would perfectly mirror the processes of intelligible human reasoning. It is this plan that has led some to believe that Leibniz came close to anticipating artificial intelligence. At any rate, Leibniz's writings about this project (which, it should be noted, he never got the chance to actualize) reveal significant insights into his understanding of the nature of human reasoning. This understanding, it turns out, is not that different from contemporary conceptions of the mind, as many of his discussions bear considerable relevance to discussions in the cognitive sciences.
4. Perception and Appetition
What do we find in the human mind? Representations on the one hand, and tendencies, inclinations, or strivings on the other, according to Leibniz. Or, to put this in Leibniz's more customary terminology, what is found within us is perception and appetition. For human minds count for Leibniz as simple substances, and, as he says in a letter to De Volder, “it may be said that there is nothing in the world except simple substances, and, in them, perception and appetite.” (30 June 1704)

Perception has already been discussed briefly above. But it will be advisable to consider also a definition from a letter to Des Bosses (and echoed in many other passages), in which Leibniz discusses perception as the representation or “expression” of “the many in the one” (letter to Des Bosses, 11 July 1706). We shall return to this definition below. Appetitions are explained as “tendencies from one perception to another” (Principles of Nature and Grace, sec.2 (1714)). Thus, we represent the world in our perceptions, and these representations are linked with an internal principle of activity and change (Monadology, sec.15 (1714)) which, in its expression in appetitions, urges us ever onward in the constantly changing flow of mental life. More technically explained, the principle of action, that is, the primitive force which is our essence, expresses itself in momentary derivative forces involving two aspects: on the one hand, there is a representative aspect (perception), by which that the many without are expressed within the one, the simple substance; on the other, there is a dynamical aspect, a tendency or striving towards new perceptions, which inclines us to change our representative state, to move towards new perceptions. (See Carlin 2004.)

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History of Mathematics / History of Calculus
« on: January 13, 2015, 04:32:14 PM »
"The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty, and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities."


The discovery of calculus is often attributed to two men, Isaac Newton and Gottfried Leibniz, who independently developed its foundations. Although they both were instrumental in its creation, they thought of the fundamental concepts in very different ways. While Newton considered variables changing with time, Leibniz thought of the variables x and y as ranging over sequences of infinitely close values. He introduced dx and dy as differences between successive values of these sequences. Leibniz knew that dy/dx gives the tangent but he did not use it as a defining property. On the other hand, Newton used quantities x' and y', which were finite velocities, to compute the tangent. Of course neither Leibniz nor Newton thought in terms of functions, but both always thought in terms of graphs. For Newton the calculus was geometrical while Leibniz took it towards analysis.
It is interesting to note that Leibniz was very conscious of the importance of good notation and put a lot of thought into the symbols he used. Newton, on the other hand, wrote more for himself than anyone else. Consequently, he tended to use whatever notation he thought of on that day. This turned out to be important in later developments. Leibniz's notation was better suited to generalizing calculus to multiple variables and in addition it highlighted the operator aspect of the derivative and integral. As a result, much of the notation that is used in Calculus today is due to Leibniz.

The development of Calculus can roughly be described along a timeline which goes through three periods: Anticipation, Development, and Rigorization. In the Anticipation stage techniques were being used by mathematicians that involved infinite processes to find areas under curves or maximaize certain quantities. In the Development stage Newton and Leibniz created the foundations of Calculus and brought all of these techniques together under the umbrella of the derivative and integral. However, their methods were not always logically sound, and it took mathematicians a long time during the Rigorization stage to justify them and put Calculus on a sound mathematical foundation.

In their development of the calculus both Newton and Leibniz used "infinitesimals", quantities that are infinitely small and yet nonzero. Of course, such infinitesimals do not really exist, but Newton and Leibniz found it convenient to use these quantities in their computations and their derivations of results. Although one could not argue with the success of calculus, this concept of infinitesimals bothered mathematicians. Lord Bishop Berkeley made serious criticisms of the calculus referring to infinitesimals as "the ghosts of departed quantities".

Berkeley's criticisms were well founded and important in that they focused the attention of mathematicians on a logical clarification of the calculus. It was to be over 100 years, however, before Calculus was to be made rigorous. Ultimately, Cauchy, Weierstrass, and Riemann reformulated Calculus in terms of limits rather than infinitesimals. Thus the need for these infinitely small (and nonexistent) quantities was removed, and replaced by a notion of quantities being "close" to others. The derivative and the integral were both reformulated in terms of limits. While it may seem like a lot of work to create rigorous justifications of computations that seemed to work fine in the first place, this is an important development. By putting Calculus on a logical footing, mathematicians were better able to understand and extend its results, as well as to come to terms with some of the more subtle aspects of the theory.

When we first study Calculus we often learn its concepts in an order that is somewhat backwards to its development. We wish to take advantage of the hundreds of years of thought that have gone into it. As a result, we often begin by learning about limits. Afterward we define the derivative and integral developed by Newton and Leibniz. But unlike Newton and Leibniz we define them in the modern way - in terms of limits. Afterward we see how the derivative and integral can be used to solve many of the problems that precipitated the development of Calculus.

11
Basic Maths / Number System
« on: January 13, 2015, 04:22:34 PM »
   
THE REAL NUMBER SYSTEM

The real number system evolved over time by expanding the notion of what we mean by the word “number.” At first, “number” meant something you could count, like how many sheep a farmer owns. These are called the natural numbers, or sometimes the counting numbers.

Natural Numbers

or “Counting Numbers”
1, 2, 3, 4, 5, . . .

The use of three dots at the end of the list is a common mathematical notation to indicate that the list keeps going forever.
At some point, the idea of “zero” came to be considered as a number. If the farmer does not have any sheep, then the number of sheep that the farmer owns is zero. We call the set of natural numbers plus the number zero the whole numbers.

Whole Numbers

Natural Numbers together with “zero”

0, 1, 2, 3, 4, 5, . . .

Integers

Whole numbers plus negatives

. . . –4, –3, –2, –1, 0, 1, 2, 3, 4, . . .

Rational Numbers

All numbers of the form , where a and b are integers (but b cannot be zero)

Rational numbers include what we usually call fractions
RESTRICTION: The denominator cannot be zero! (But the numerator can)
If the numerator is zero, then the whole fraction is just equal to zero. If I have zero thirds or zero fourths, than I don’t have anything. However, it makes no sense at all to talk about a fraction measured in “zeroths.”

Fractions can be numbers smaller than 1, like 1/2 or 3/4 (called proper fractions), or they can be numbers bigger than 1 (called improper fractions), like two-and-a-half, which we could also write as 5/2
All integers can also be thought of as rational numbers, with a denominator of 1:



This means that all the previous sets of numbers (natural numbers, whole numbers, and integers) are subsets of the rational numbers.

Now it might seem as though the set of rational numbers would cover every possible case, but that is not so. There are numbers that cannot be expressed as a fraction, and these numbers are called irrational because they are not rational.


Irrational Numbers

Cannot be expressed as a ratio of integers.
As decimals they never repeat or terminate (rationals always do one or the other)
Examples:



     3/4 Rational (terminates)



     2/3   Rational (repeats)



5/11   Rational (repeats)



5/7 Rational (repeats)



  square root of 2: Irrational (never repeats or terminates)




3.1416    Irrational (never repeats or terminates)


The Real Numbers

Rationals + Irrationals
All points on the number line
Or all possible distances on the number line
When we put the irrational numbers together with the rational numbers, we finally have the complete set of real numbers. Any number that represents an amount of something, such as a weight, a volume, or the distance between two points, will always be a real number. The following diagram illustrates the relationships of the sets that make up the real numbers.





12
Public Health / Beef Chili With Beans
« on: January 12, 2015, 11:50:38 AM »
This hearty chili is sure to heat things up so it's the perfect winter meal. Onions and garlic combine nicely with the chilis and kidney beans.

Ingredients:

2 lbs (1 kg) stewing beef, cut into 1/2-in. (1-cm) chunks
1/4 cup (50 mL) all-purpose flour
1 tsp (5 mL) salt
1/4 tsp (1 mL) pepper
2 tbsp (25 mL) vegetable oil
3  onions, chopped
4  cloves garlic, finely chopped
2 tbsp (25 mL) chili powder
1 tsp (5 mL) ground cumin
1 tsp (5 mL) dried oregano
1  28 oz (796 mL) can plum tomatoes, chopped or puréed with juices
1 cup (250 mL) beef stock or water
1 to 2 tsp (5 to 10 mL) puréed canned chipotle chilis or to taste—optional
2 cups (500 mL) cooked red or white kidney beans (one 19 oz/540 mL can, drained and rinsed)
Toppings: sour cream or yogourt, grated smoked Cheddar, chopped fresh tomatoes, corn niblets, chopped fresh cilantro and chopped green onions.

Directions:
Toss beef with flour, salt and pepper. Place in a strainer and shake off any excess flour.
Heat oil in a Dutch oven or deep skillet. Brown meat, in batches if necessary. Remove meat from pan and discard all but 1 tbsp (15 mL) oil. Add onions and garlic and cook gently about 5 minutes until fragrant and tender. Add chili powder, cumin and oregano. Cook gently one minute.
Add tomatoes, stock and chipotles. Bring to a boil. Add browned beef. Cover surface of meat with a round of parchment paper and cover with a lid. Cook in a preheated 350°F (180°C) oven 1 1/2 to 2 hours or until very tender.
Add beans and bake, uncovered, until thick about 20 to 30 minutes.  Taste and add salt and pepper if necessary.
Serve in individual bowls and let guests add their own toppings.

13
Nutrition and Food Engineering / Pumpkin Cheesecake
« on: January 12, 2015, 11:44:04 AM »
Make your holiday feast complete with a spin on the traditional pumpkin pie. Your guests won't believe this delicious pie is a reduced-calorie dessert.

Ingredients:

40 gingersnap cookies
1  cup  granulated sugar
1⁄2 cup  toasted walnuts, cooled completely
1⁄4 cup  butter, melted
2 tbsp  water
2 tsp  ground cinnamon
3⁄4 cup  pumpkin puree
3 eggs
2 pkgs  Neufchâtel cheese, softened
1 pkg  fat-free cream cheese, softened
1 tbsp  vanilla extract
1⁄2 tsp  kosher or sea salt
1& 1⁄2 tsp  pumpkin pie spice

Directions:
Preheat oven to 325°F. Use 1–2 large pieces of aluminum foil to cover bottom and sides of 9-inch springform pan. (This technique will reduce leaks when using a water bath.) Add gingersnap cookies and walnuts to blender and run for 5 seconds.

Add butter, water, and cinnamon and run for 10 seconds. Press crust evenly into springform pan along bottom and up sides about 1 inch.

Clean blender, and add pumpkin, eggs, Neufchatel cheese, cream cheese, sugar, vanilla, salt, and pumpkin pie spice. Secure lid and blend. Pour filling over crust. Place springform pan inside of larger pan that is 2–3 inches deep. Pour approximately 1 inch of boiling water into larger pan. Carefully place pan in oven, and bake for 90 minutes. (The center of cheesecake will jiggle but will complete cooking during the cooling process.)

Cool cheesecake completely, and then place in refrigerator until sufficiently chilled, about 10–12 hours. Serve with your favorite whipped cream or caramel topping.


link:http://www.readersdigest.ca

14
Nutrition and Food Engineering / Tomato Cheese Soup
« on: January 12, 2015, 11:27:27 AM »
Ingredients:
1    medium onion, chopped
45 ml / 3 tbsp    olive oil
500 ml / 2 cups    peeled, seeded and chopped tomatoes
500 ml / 2 cups    chicken stock
75 ml / 1/3 cup    35% cream
375 ml / 1 1/2 cups    grated goat cheese
To taste    freshly ground pepper
15 ml / 1 tbsp    chopped chives

Directions:
In a saucepan, wilt the onion in the oil.

Add the tomatoes and stock, bring to a boil, reduce the heat to low and simmer 10 minutes

Add the cream, cheese and pepper. Stir well to melt the cheese.



Serve drizzled with oil and garnished with chopped chives.

15
Nutrition and Food Engineering / Chicken Vegetable Soup With Noodles
« on: January 12, 2015, 11:19:05 AM »
Ingredients:
1 tablespoon vegetable oil
1 medium onion, coarsely chopped
3 carrots, peeled and diced
1 medium celery stalk, diced
2 cans (410 mL each) fat-free low-sodium chicken broth
1 can (410 mL) diced tomatoes, undrained
8 ounces chicken breast, skin removed
1 small turnip, peeled and diced
1 teaspoon dried basil, crumbled
1 1/2 cups thin noodles
1/4 teaspoon fresh ground black pepper


Directions:
1. Heat oil in a large saucepan over medium heat. Add onion, carrots, and celery and sauté 5 minutes or until softened. Add broth, tomatoes, chicken, turnips, and basil. Simmer, uncovered, 30 minutes or until chicken is cooked through.

2. Transfer chicken to a plate. When cool enough to handle, remove bones and coarsely chop meat. Return to pan, add noodles, and cook 4 minutes or until tender. Add pepper and serve.


Note:Root vegetables like carrot and turnip add an earthy flavour to this traditional chicken soup.

link:http://www.readersdigest.ca/


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