A Mathematical Visit

Hello reader:

In September 11, I visited my former high school teacher Mr Grosinger. The purpose of the visit was to catch up in our current projects and to learn how to drive standard transmission (stick). In my visit I meet Mr. Yoav Benari, who is my teachers girlfriend's dad. He is a very interesting man. Dr. Benari received both an undergraduate and graduate degree from Princeton University. One thing we spoke about was my visit to the Math Museum. I explained about the Catalan number. In response, he talked about the mathematical constant pi, and Archimedes. 

Before I go in detail about Archimedes, Mr. Benari has a blog called FinancialGauge. In this blog, he analysis the financial market as well as understanding current market development.

To continue with Archimedes. He was a Greek mathematician, physicist, inventor and astronomer. His discoveries were admirable. Some of the most admirable to me are as followed:

1. Archimedes' Principle which states " Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object." By dividing different shapes into small strips he determined centers of gravity and buoyancy.  

2. Claw of archimedes. the claw was a weapon design to defend the city of Syracuse. The weapon consists of a crank-like arm, which lifted ships out of the water and possibly sinking it.

3. Personally the one I enjoy reading the most about was about Pi. He developed the first method for calculating the value of Pi with greater precision then those of which had already existed. The reason why I enjoyed searching for Pi was because Mr. Benari asked me an interesting rhetorical question:  how can we precisely determine the value of a circles circumference or area when Pi itself is an irrational number. Hopefully, that question will motivate you to look for an answer. 

As a final note, in the museum I was asked how many mathematicians did I know of. I had a very sad answer... The same answer I had when Mr. Benari asked me if I knew who Archimedes was, I just didn't know. This triggered something, my question is: Why are we only taught the very important mathematical equations that have helped the progression of not only math but science as well, yet we are not taught about the great minds who came up with them, or why? 

Therefore let me ask you, how many mathematicians can you mention with their respective theory or what they are known for?

If you are lost, here are a few suggestions: Descartes, Fermat, Pascal, Newton, Leibniz, Euler, Gauss, Riemann, Euclid, Pythagoras of Samos. 

801 Things You Should Know: Part 4

Hello reader:

This the fourth part of 801 Things You should Know by David Olsen.

1.Philosophy

Animism- is the belief that physical entities, such as animals, plants, and rivers, posses a spirit.

2.History

The American crisis- is a series of sixteen pamphlets written and published by Thomas Paine during the American Revolutionary War. He wrote about the need for revolution and human freedom.

3.Business and Economics

Amortization- is a process of decreasing a debt by making payments over a period of time.

4.Art and Literature

Acropolis- is a settlement, such as a citadel, built in a hill for defense purposes.   

5.People and Culture

Allen, Woody- he is an American screenwriter, actor, comedian and director. He has won multiple awards. One of his fourty films, Annie Hall, won him 4 Oscars in 1977. Additionally, comedy central ranked him fourth of the greatest stand-up comedian. A UK survey ranked him third.

6.Politics

Apartheid- A system of racial segregation enforced by the government of the National Party of South Africa.

7.Science and Technology

Alpha radiation- is a type of radioactive decay. A radioactive particle decays in to an isotope and an alpha particle. Alpha particles are made of two neurons and two protons.

8.Social Science           

           

Animism

Volunteering at the Museum of Mathematics

Hello Reader:

In September 4th, I volunteered at the The Museum of Mathematics. The experience was rewarding . Not only did I learn about applied mathematics but I also was able to attended a presentation by Alissa Crans. The presentations name was "A Surreptitious Sequence." She presented the Catalan numbers.  The sequence starts by 1,1,2,5,14,42, ... .The main purpose of the presentation was to show in what occasions does the sequence occurs.s

For example 1:

Let say we want to triangulate a convex polygon with n+2 sides you can obtain the catalan numbers. Here is a illustration

* I apologize for my lack of drawing skills. 

Example 2

Suppose you have a set of n + 1 numbers to multiply together, meaning that there are n multiplications to perform,without changing the order of the number.  Here are the possible multiplication

n=0   (a)        1 way

n=1   (a)(b)   1 way

n=2   (a*b)c , a(b*c)    2 way

n=3 ((a*b)*c)*d , (a*b)(c*d), (a*(b*c))*d) , a*((b*c))*d), a*(b*(c*d)) 5 ways

n=4 is for you to try. 

If you want to continue looking for more examples just search online you will find many examples. 

801 Things You Should Know: Part 3

Hello reader:

This the third part of 801 Things You should Know by David Olsen.

1.Philosophy

Agnosticism- Is skeptical view about truth of certain things. For example, the existence or nonexistence of a deity.

2.History

Alien and sedition acts- a series of law signed by U.S. president John Adams to restrict activities of those who criticized his federalist ideas and support the French revolution.

3.Business and Economics

American Stock Exchange- (AMEX) is the second-largest stock exchange in the US,     located in NYC.

4.Art and Literature

 Achilles' Heel- was the weak point of the Trojan War hero Achilles of the Greek mythology. Now the term is used as a person’s vulnerable spot.  

5.People and Culture

Ali, Muhammad- one of the greatest boxers of all time. He won three world-heavyweight championships. However, he was not only known for his ring abilities but for his thought. He created controversy of religious freedom and racial justice.

6.Politics

          Ad Nauseam- something repeatedly said to the point of sickening  

7.Science and Technology

Aerobic- has four definitions. However, there only two related to science. One is organism aerobic, which are organisms that need oxygen to live. Second is aerobic respiration. This is a form of cellular respiration in which oxygen is used to survive. 

8.Social Science           

Alter ego- latin for "another I." - is a second self usually different from its original or normal personality.  

Yerba Mate Vocabulary

Hello reader:

This is the second post on Yerba Mate. As the title says, this post consists of some words I came across while reading the articles and did not understand.

Caffeoyl (caffeic acid) -is an organic yellow compound found in all plants. It is a key intermediate in the biosynthesis of lignin.  

Lignin- is a chemical compound that supports the strengthening of wood          (xylem cells) in trees.

Xylem cell- is one of the two types of tissue carriers in vascular      plants. Its function is to transport water and nutrients

Chlorogenic acid- is a complex ester of polyphenolic caffeic acid and cyclitol. Also, is another intermediate in the biosynthesis of lignin.

Phenolic- is a white crystalline which acts as a disinfectant in organic synthesis.

Ester- is a chemical compound derived from reacting an acid and an alcohol. In nature ester are in general, fat.

Quinic Acid- is a cyclitol. It is present in cinchona bark, coffee beans, and the leaves of many plants. In general, it is an intermediate product in the biosynthesis of aromatic compounds in  higher plants and some micro organisms.

Cyclitol- are cycloalkanes containing a hydroxyl group on each of the three or more ring atoms. As well as an osmoprotectant.

Cycloalkanes- a saturated hydrocarbon compound. Known for their constant polygonal form.    

Osmoprotectant- are small molecules that act as osmolytes and help organisms survive extreme osmotic stress.

Osmolyte- are compounds affecting osmosis. Their role is to maintain cell volume and fluid balance.

Osmotic shock (osmotic stress)- is a sudden change in the solute concentration around a cell, causing a rapid change in the movement of water across its cell membrane.

Oxidative stress- is an imbalance between the systematic manifestations of reactive oxygen species and biological system’s ability to readily detoxify the reactive intermediate or repair the resulting damage. In other words, is a toxic effect through the production of peroxides and free radicals which damage component of the cell. In addition, it disrupts cellular signaling.

Flavonoids- are a large part of the water-soluble plant pigments that are beneficial to human health. It has antioxidant, antiviral, and anti-inflammatory properties.

Xanthine- is a chemical compound found in human tissue and fluids, and other organism. They stimulate the central nervous system, stimulate cardiac muscles and relax smooth muscles.

Saponin- are chemical compounds found in natural sources. It is particularly abundant in plant species. In general, they are characterized by their ability to form emulsions, and durable foam in watery solutions.

Dsylipidemic- an abnormal amount of lipids in the blood.

Lipids- are organic compounds that are greasy to the touch and       insoluble in water. However, they are soluble in alcohol and ether.

Legumes- any plant of the leguminosae family. For example, beans, nuts, lentils, etc

Antioxidant- a chemical compound that protects the body from oxygen radical-induced damage.

               

Yerba Mate

Hello Reader:

For a week, I gathered information about a drink ingredient used at the restaurant In which I am currently employed. The ingredient is called Yerba Mate, for more info just click on yerba mate. I attached a link to Wikipedia. However, I am warning you, I do not fully trust wiki, but it will give you a quick overview of what yerba mate is and where it is originated. Anyways, I was reading about it and I realized yerba mate has a few interesting health benefits. At that moment, I thought it was fascinating and then I started gathering information.

This post consists of a quick summary of what I found. Nevertheless, at the end of the quick summary I wrote my resources. The only difficulty you may encounter with the resources I used to do my research is that I searched them using my NJIT library account. Therefore, I do not know if you will be able to read the resources completely.

Yerba Mate (Illex Paraguariensis)

Mate is green plant used as an herbal tea. The tea is widely consumed in South America, countries such as Argentina, Brazil and Uruguay. Some of the health benefits of the tea are: high in antioxidant activity, weight management and obesity, and carcinogenesis.

The chemical isolation consist of

A.    Caffeoyl derivatives

a.       Chlorogenic acid

b.      Caffeic acid

c.       Dicaffeoyl quinic acid

B.     Flavonoids

a.       Rutin

b.      Quercetin

c.       Kaempferol

C.     Xanthines

a.       Teophylline

b.      Theobromine

c.       Caffeine

D.    Saponins

a.       Triterpenoid

E.     Minerals

a.       Aluminum

b.      Chromium

c.       Copper

d.      Iron

e.       Manganese

Resources- Here is the list of the 4 articles I summarized about Yerba Mate. However, I encourage you to continue searching because there is a lot of information about yerba mate. I did not include everything I found but among it you can find  mate can be used to prevent epileptic seizure and mate extracts can be used for organic pharmaceutical medicine or can be added to processed food to increase its nutritional quality .

“Applied Nutritional investigation: Association of Mate Tea intake and dietary intervention and effects on oxidative stress biomarkers of dyslipidemic subjects”

            In summary, its a 90 day test of yerba mate tea on 74 dsylipidemic volunteers. The subjects were divided into 3 groups: Mate Tea (MT), Dietary Intervention (DI), and Mate Tea with dietary intervention (MD). MT and MD consumed one liter per day of mate tea. MD and DI were instructed a healthy diet, which consist of increasing their intake of fruit, legumes, and vegetables and decrease cholesterol, saturated and unsaturated fat. They were assessed at the beginning of the study and after in the 20th, 40th, 60th and 90th day. The results showed an increase in serum antioxidant and a decrease in cholesterol. First, regardless or independently of the dietary intervention, the subjects increased their blood antioxidant, which lowered oxidative stress. In the other hand, with dietary intervention, they increased the antioxidant capacity and decreased the consumption of total and saturated fats. In a like manner, these results were consistent with result from other studies and similar beverage rich in antioxidant, such as green tea. In the same study, they also found a low GHS peroxidase concentration, which is considered a risk factor for the development of cardiovascular disease (CVD). Additionally, a slightly increase in serum paraoxonase 1 (PON1) was shown. PON1 acts as a protection against CVD. At last, they suggest a more strict dietary approach is needed to observe a greater increase in PON1.

“Antioxidant activity of Illex Paraguariensis and related species”

            In summary, they examine antioxidant activity of yerba mate and related species. The related species are the following:

·         I Theezans C. Martis ex Reisseck

·         I Dumosa Keisseck Var Dumosa

·         I Argentina Lillo

·         I Brevicuspis Reiseeck

·         I Pseudobuxux Reisseck

Additionally, they examine caffeoyl-derivatives. The results showed I Paraguariensis has the highest antioxidant activity. Also, antioxidant properties remain after the tea is prepared. At last, they speculate it can contribute to human antioxidant defense.

“Rearching on new species of ‘Mate’, (Illex Brevicuspis)”

            The study was taken to isolate, identify and quantify polyphenolic compounds in the plant. The chemical isolation they found was shown above. Nevertheless, they stated that the tea has high antioxidant activity, intestinal propulsion activity and showed no sign of toxicity.

“Yerba Mate Tea: A comprehensive Review on Chemistry, health implications, and technological considerations” This is my favorite article. The article is very complete in the sense that it has a complete list of all the chemical compounds in mate. In addition, it has a lot of charts with information and comparison with other teas.  

            The article is a review that presents the usage, chemistry, biological activities, health effects, and some technological consideration for processing yerba mate.  The final consideration of the article is mate diverse concentration of biological compounds, such as xanthenes, theobromine and theophylline are attributed to its health benefits. On top of that, its active compounds make it ideal for compound extraction and use it in foods and supplements. In conclusion, cancer development from mate can be a result of contaminants involve in the process procedures. As an alternative, a more optimized process  and good quality control is needed to eliminate contaminants.