Law of Exponents

Original notes by: Lauren F.
Typed up by: Katelyn C.

Laws of Exponents


The rules we have tell us what to do when:
Product, Quotient, Power, Inverse, Zero exponent:
The exponent appears as anyone of these “positional” terms

What is a product? Here, and generally, it is the result of terms into a sum or “summarizable” form.
Remember that in our complex number system, we have different forms and position of our terms in those formulae to represent numbers that are rational (like ½ or .5(diff. notation)).

While other values such as π are irrational, we nonetheless have a “decadecimal” numeric system(complex numbers) that follow the form ab+i

The product rule tells us:

a m x a n = am+n Add exponents

22 x 23
= (2×2)(2x2x2) = 25

Alternatively, you might see the number 25 as 32. They are the same number, as it is written in exponent, notational form.

We often need exponents to shorten or abbreviate our calculations for large exponential values. So, there comes a functional necessity to use alternate forms of representing numeric values, as we quantify different problems.

If we were given 64 as a value, we want to write it as an exponent. We would take a look at prime factorization

64
↙ ↘
32 x 2
↙ ↘ ↓
16 x 2 2
↙ ↘ ↓ ↓ *All numbers multiplied
8 x 2 2 2 together in each row
↙ ↘ ↘ ↓ ↙
4 x 2 2 2 2
↙ ↘ ↓ ↓ ↓↓
2 x 2 2 2 2 2 = 26

If you did this for 32, you’d get 24

(2×2) 2x2x2
↘↙ ↘ ↙
4 x 8 = 32

PRACTICE:
42x 47=49
58x 52x 51=511
34x 3-2=32

Grade 6 Mathematics Lessons: Module 4

by: Lauren F.
Typed up by: Katelyn C.

Grade 6 Mathematics; Module 4

Expressions and Equations:

In this module, you will add to your arithmetic skills, the ability to:

Use variables as substitutes OR “standins” for some numbers #UNKNOWNVARIABLES
Operations in verbal expressions
Relationships of operations and equivalent expressions (Manipulating numbers —>> Manipulating Expressions)
Read, write, and evaluate expressions in order to develop formulas
True and false number sentences (When substituting for a variable —>> True or false? #TRUESENTENCE #EXPRESSIONS
Arithmetic problems
Identities (Arithmetic)
Bar Models
Algebra to solve 1-step, 2-step, and multi-step equations

(Hashtags signify important terms that are really useful to help you do well)

Bar Models:
A visual representation of a number using unit. This can be cubes, lines (consisted of 10 cubes), sheets (of 100 cubes), and boxes (of 1000 cubes).
These models can be used as a visual/pictorial tool in solving addition and subtraction (and arithmetic operations).

*Use this link to help you: Introduction to the Bar Model

Now, let’s solve a “Real World” problem using Bar Models and Algebraic Reasoning:

Q: Ray has 16 more game cards than May. If they have a total of 48 game cards (remember, altogether=total), find the number of game cards Ray has.

A: This is the +16 in your resulting Algebraic equation
Ray: ↙
X
16
COMBINE THE TWO AND HAVE THEM EQUAL 48
May:
X

*Set up the (X+16)+X=48 expression, algebraically*

*The X in the parenthesis and the X outside of the parenthesis get added together because they are “like terms,” both consisting on “X”*

What gets done 2X + 16 = 48 on one side, must
“balance” on the – 16 -16 other side of the expression

Divide on both 2X = 32 Divide out the
side of = sign /2 /2 coefficient of X

X = 16

When you plug this answer back into the bar model, Ray would have a total of 32 game cards, as the X would equal 16, and it’s being added with the 16 already there because it originally said he had 16 more game cards than May did. 16+16=32. Plugged into May’s Model, she would have 16 cards because she only has the one X. All together, Ray’s 32 cards and May’s 16 equal to the total of 48.

Let’s look at another example:

Joan has 3 more pencils than Lucy. Joan has 5 pencils. How many pencils does Lucy j have?

Joan:
5
*Can you solve it?
Lucy:
X
—-3—-

Algebraic Thinking in Our Own Words….

Let’s talk about problem solving. When we are problem solving, we use what we know OR are “GIVEN” as information to figure out what we don’t know, OR an “unknown” value

We can call the variable X an unknown for now!

Also, we should think about X and Y variables on a graph, and begin to keep in mind how they correspond to one another. This will be especially useful learning to determine patterns within data that is collected. It will be important to know how a value you get for X corresponds to Y value(s) on a coordinate plane, or a graph.

Algebra to solve 1-step, 2-step, and multi-step equations

1-step: In a one-step equation, you will only need to perform one step in order to solve the equation
EX: 3X = 12 3(4) = 12
/3 /3 12 = 12 ✔
X = 4

*It’s important to keep in mind when solving an equation that you should be getting the variables on one side of the equal sign and the known numbers on the other side*

2-step: EX: 20X + 5 = 105
– 5 -5

20X = 100 Divide out the coefficient of X, which in this case
/20 /20 is 20!
X = 5

Now let’s check if our answer is right! We can do this by plugging in our answer e for every X there is, in the original equation

20(5) + 5 = 105
100 + 5 = 105
105 = 105 ✔

The above equation requires 2 steps. Remember that you must use the OPPOSITE mathematical operation in order to remove a number from one side of the equation.

For example, because the 5 was added to the 20X in our practice problem, we had to subtract 5 in order to remove it from its side, and we also had to subtract 5 on the other side too!

When you solve 2 step equations, REMEMBER THIS RULE:

*Always remove the constant first using either addition or subtraction*

Let’s try another 2-step….

-5X -4 = 46
1. Remove the 4 first 1. +4 +4
by adding it to both
sides since it’s originally
being subtracted
-5X = 50 *We are not subtracting 5, but instead
2.Simplify and remove 2. /-5 /-5 dividing 50 by -5 (Negative five)*
the coefficient -5 from
both sides of the equation
to get X alone, usually on
the left hand side (LHS).
X = -10

Check by substituting the value you got for X into the original equation #STANDIN

RULE: Negative number x negative number = positive number

-5X – 4 = 46
-5(-10) – 4 = 46
50 – 4 = 46
46 = 46 ✔

3-Step and multiple step algebraic expressions:

Solving 3 step equations uses the same buck tracking method as 2-step equations

2m + 3 = 3 ←This numerator value must be /5 divisible by 5 to equal 3

How do we get m?

2m + 3 = 3 Set 3 over 1 and cross multiply
/5 /1

15 = 2m + 3 Now we can solve in 2-steps….
-3 -3 subtract out 3!

12 = 2m Divide by the coefficient 2 to get m
/2 /2 by itself on one side of the equal sign

6 = m OR m = 6 REORDER THE TERMS

CHECK: 2(6) + 3 = 3
/5

12 + 3 = 3
/5

15 = 3
/5
3 = 3 ✔
Arithmetic Properties and Identities

The Identity Property for Addition tells us that zero added to any number is the number itself
EX: 5+0=5; 3+0=3; 295+0=295

The Identity Property for Multiplication tells us that the number 1 multiplied by any number gives us the number itself
EX: 5×1=5; 3×1=3; 295×1=295

*For some more practice, visit:
Properties of real numbers practice

TRUE and FALSE number sentences:

A number sentence is the most concrete version of an equation. It has the very important property that it is always TRUE or it is always FALSE, and this property distinguishes it from a generic equation

Let’s look at this in an example;
4 + x = 7
If we substitute 3 in for x, would it make the equation true or false?

It would make it true because both sides would evaluate to 7. 7=7

But, if we substitute 4 in for x, it would make a false number sentence, because 4+4 would equal 8, not 7.

*PRACTICE:
Reading and Writing Algebraic Expressions

Relationships of Operations and Equivalent Expressions:

Changing the order of addends does not change the sum

Commutative Property of
Addition

Use for mental math calculations:
13+29+17 = 13+17+29 =
30+29= 59
Numbers
3+5 = 5+3 EQUALS 8 EITHER WAY
Algebra
a+b = b+a

Relationships & Biodiversity

Original notes by: Lauren F.
Typed up by: Katelyn C.

Relationships and Biodiversity

Molecular Evidence

What are some markers of Biodiversity that have been identified in the Natural World?

Well, let’s look at a few:
Phylogenetic distance; Phylogeny- The study of the evolutionary history and relationships among individuals or groups of organisms
Fossil Record- imperfectness
*Genetic Analysis- Mathematical Sequencing- Technology*
Proteome (complete set of proteins expressed by an organism); Microbiome (The genetic material of all the microbes); Analysis (Current)

Questions about proteins?
-Proteins contain Carbon, Hydrogen, Oxygen, and Nitrogen. Some even contain Sulfur.
-Proteins are mainly used for the growth and repair of cells.
-Their building blocks are called amino acids, in which there are 20 different kinds
-Proteins are found in hemoglobin(carries oxygen), skin pigments(melanin), hormones, antibodies, enzymes, hair/nails, and cell membranes
-Proteins are composed of one or more polypeptide coiled or folded in a specific way. Polypeptides are chains of amino acids
What happens when the body takes in proteins (pick a type of amino acid) and digests it?
-When the body takes in a protein it sends it to the stomach, where through the process of mechanical and chemical digestion will proteins be broken down small enough to pass through cell membranes into the body tissues to be used as nutrients
Are there examples?
The digestive process takes, on average, 12-24 hours. Proteins begin their journey, as do all nutrients, and travel to the stomach. Here, hydrochloric acid and pepsin break down protein into peptide chains (A peptide bond is the bond between 2 amino acids, so a peptide chain would be a chain link of peptide bonds). Proteins finish their journey in the small intestine, where peptidases snip peptides into amino acids for absorption
How do proteins interact with other proteins?
As we’ve read from earlier, proteins are typically linked together, which helps us to see how they never act alone. These links are called, as previously mentioned, peptide bonds. These are formed by a biochemical reaction, called dehydration synthesis, where one water molecule is extracted as it joins the amino group of one amino acid to the carboxyl group of a neighboring amino acid.
What could a mutation do in terms of its effect on a protein?
(This information came from help from the below link)
There are many different types of mutations that could affect protein function. A missense mutation changes an amino acid to another amino acid. This may not have a drastic effect on the protein, depending on what the amino acid actually does. A nonsense mutation changes an amino acid to a STOP codon, resulting in premature termination of translation. A silent mutation doesn’t change the amino acid, but can have a phenotypic effect by speeding up or slowing down protein synthesis. A frameshift mutation consists of a deletion or insertion of a number of bases that is not a multiple of 3. This will usually introduce premature STOP codons, as well as lots of amino acid change

What are plant proteins? Could they be interacting with our immune system? I.e allergies- food & environmental

Plant proteins are proteins that originate from plants. They will interact with our immune system, as the nutrients we obtain from these plant proteins from digestion will greatly help to make us feel stronger and better. These proteins could also trigger an allergic response, as they are a foreign entity that would enter our body. Antibodies can bind to the surface of mast cells, which contain histamine and can trigger an inflammatory response.

Biodiversity
Measure of type of organisms in a location

Eco-stability- When the different groups of organisms in an environment and the resources are in an equilibrium of each other

Darwinian Finches- Charles Darwin observed finches on the Galapagos Islands, and noticed how the finches on one island were different than those on another island. The differences were most notable in the beaks that the finches had. Some beaks were short and fatter, and some were longer and thinner. This was because finches on one island had more access to nuts and berries, while the others had better access to eating things like insects. He concluded that these species had adapted to the environment in which they were living in, and that not only the finches did this, but ALL species living on Earth arrived to their current form through centuries of Evolution and Adaptation.

Evolution by Natural Selection- 1. Some characteristic of trait (variation) must exist that is 2. at least partially hereditary. 3. Some variants must survive and reproduce in greater numbers

A population undergoes Evolution

We also see cool relationships between living systems. One modality of interconnection- symbiosis- shows the delicate balance and intricacies of the natural world at its finest

Think about the importance of balance and homeostasis in systems. A system must “calibrate” in order to work efficiently. Like a suspension bridge

In the case of a bridge, there is a range of weight/force it is built to withstand

Is it OK to think about our genetic code like this bridge? A system- a sequence of codes that allows for excess force, integration, and possibly even- dare I say it- expansion?

Think of the Prefrontal Cortex- and think neuroexpansion- think “junk” DNA as a seed that will emerge under the right circumstances as an aggregate of mutation and heredity- which is only plausible as genetic sequences are exponential functions.

Next, we must think about limits, and wonder if this is the sort of “critical density” in which the code mutates to the point that one mutation works with another to produce a “tertiary” effect- therefore, we observe neurological phenomena such as synesthesia. Synesthesia is a neurological condition in which stimulation of one sensory or cognitive pathway leads to automatic, involuntary experiences in a second sensory or cognitive pathway.

Newtonian Influence into the Modern Era by Academic Tutors 101 (L.F., 2009)

Newtonian Influence into the Modern Era
by Academic Tutors 101 (L.F., 2009. Revised 2017)

The Legacy behind the Man: Sir Isaac Newton
One of the most infamous scientists in all of human history is Sir Isaac Newton. Newton was born in the Julian year of 1642 on the 25th of December, a date that is equivalent to January 4, 1643 on the Gregorian calendar. [1]

“Isaac Newton was born prematurely to a widowed mother, in Woolsthorpe Manor in Lincolnshire, England.[2]

Early in his life, Newton’s mother would remarry and leave him to live with his Grandmother at Woolsthorpe. He would receive an education locally and eventually attend as school at Gratham, where he resided with a local apothecary.[3]

In 1661, he began his attendance at Trinity College in Cambridge, England. There Dr. Isaac Barrow would come to be an important influence as his mentor, professor and friend.
His genius soon became obvious to many and is regarded in his uncle’s declaration, that it would be wrong “to bury so extraordinary a talent in rustic business.”[3]

In 1661, Isaac Newton left Lincolnshire to continue his studies at Cambridge. However, in 1665 and 1666, he was forced to return to Woolsthorpe to escape the outbreaks of bubonic plague. It was at Woolsthorpe Manor that Isaac Newton formulated three great discoveries; the Principle of Differential Calculus, the Composition of White Light and the Law of Gravitation.

He later observed, “In the two plague years, I was in the prime of my age for invention and minded mathematics and philosophy -more than at any time since.”[3]

Newton lived during a Historically significant epoch where Mathematics, Science, Philosophy, and the Arts synergistically enriched all of Europe leading to the culmination and convergence of major discoveries and inventions; This was the 17th century.

Newton’s life also spanned the later part of the periods known as the Renaissance and the Scientific Revolution; the Early Modern Period.[4]

Newton’s work marked the advent of early Modernism that would shape the future of Scientific advancement far into the future. Newton retrospectively influenced developments of Western Civilization into the Age of Enlightenment in the 18th, the 19th century and ultimately the Modern era. This is why today, Sir Isaac Newton is still highly regarded as one of the most ingenious men to have ever lived.

A true “Renaissance” man- a polymath, Newton took up studies as an “English Physicist, Mathematician, Astronomer, Natural Philosopher, Alchemist (an early Chemist) and a Theologian.”[1]
Newton contributed greatly to the fields of Mathematics, Physics, (Alchemy) Chemistry, Optics, Mechanics and Gravitation.

“As a natural Philosopher, Newton was concerned with the state of the natural world and the physical universe.”[5] Philosophical interests in these areas came to influence much of his work. In keeping with the ideas of the Renaissance and the Scientific Revolution, the philosophical approach to the natural world came concurrent to precursor trends in learning called, Humanism and Scholasticism. Although leading Humanists would come to reject the ideals of Scholasticism, Newton seemed to embraced both approaches to learning. It seems that his work was influenced by those who came before him- asking similar questions- including Aristotle (Aristotelianism) and Plato (Neoplatonism). In heritage, Newtonianism would come to be the term for the tradition of Newtons contribution’s to Natural Philosophy and Science.

Although a true magnate, Newton is reputed in historic accounts as a humble man of good nature – a spiritual man, and as a leading member of English Society and the greater Scientific community. In the end of his life, at the age of 85 years old, Newton said,
“I do not know what I may appear to the world, but to myself, I seem to have been only like a boy playing on the seashore and diverting myself in now and then, finding a smoother pebble or a prettier shell then ordinary, whilst the great ocean of truth lay all undiscovered before me.[3]

Newton’s Study of Optics

Newton’s contribution to advancements in Optics began with a natural curiosity about the light emitted by celestial objects, particularly the Sun. In later works he would keep focus on the heavens but shift his exploration to the forces that held the moon in place. It is clear that he also took influence in optics based upon his reading of Johannes Kepler’s geometric approach to optics and Theory of Lenses as part of his mathematical studies at Cambridge. To note – Kepler was a contemporary of the 17th century Scientific Revolution and natural philosopher, influenced by Aristotelianism (Aristotle- the first know Tutor!); The result of this influence resonated within discoveries that would overrule past philosophical approaches to similar matters of investigation, in some right.
Newton studied the optics {or as he wrote “opticks”} of visible light and its functional “relativity” to objects or matter; This led into his study of magnetism and gravity which facilitated and furthered later studies on electromagnetism and theoretical physics. (This would influence Einstein! Noble Archives: The Dual Nature of Light)

The exploration of light, by Newton, would reveal properties of magnification that suggested light did not travel the trajectory of a straight line. Leaving the question – what is the course that light travels?

To answer this question he began experiments with casting shadows through glasses filled with water and measuring light that shown through openings in glass plates. This process led into experiments with different physical objects like metal, stone, wood, ice, and their apparent relationship to light, i.e. Did the objects refract light or cast shadows? The “reaction” of these natural materials in casting shadows or conducting light would be measured and recorded according to categorical criteria such as luminosity, color, breadth and distance. The results of Newtons findings preliminarily included in Opticks: Or, A Treatise of the Reflections, Refraction’s, Inflections and Colours of Light. The Second Edition, with Additions (London: 1717)1717, in English, c. 24,028 words, The Third Book of Opticks. Part I Published in: Opticks: Or, A Treatise of the Reflections, Refraction’s, Inflections and Colours of Light, Second Edition(London: 1717) [6] concluded that rays of light bend. This came to be the basis of Newtons theory of Refraction – when the natural object comparison was made in regard to the mathematical concept of a hyperbolic plane or hyperbola. The figure of an hourglass is quite comparable to a hyperbola planar figure (see, Euclid’s Conic Sections). He found that the motion of light is equivalent in refraction to that of a hyperbola as a central figure for elliptical movement; This precluded in Isaac Newton’s letters entitled Mr. Isaac Newtons Answer to some Considerations upon his Doctrine of Light and Colors [7]

These notions evolved into the explanation for observable deformity of refraction as the mechanism for reflections in mirrors which would come to be utilized by Newton to create a more efficient telescope in 1669. See, The Newtonian telescope. Telescopes became the technological product of western civilization – being defined as an instrument in optics due to the detection of the refraction of light off of an object. Prior to this, “Johannes Kepler had developed a refracting telescope called the Keplerian Telescope as he borrowed from the previous telescopic discovery of Galileo Galilei.” [8]

Beyond this – Newton’s experiments with light as a force that bends and refracts determined its (anthropomorphically speaking) quantum nature which later revealed the physical components of refraction as particles of matter in addition to solid masses. See, Particle-Wave Duality. Eventually, all of this led to the discovery of the photon and a postulate about the boson particle! Bosons as a material particle came to be studied by Albert Einstein in his theories on particle physics; Discoveries followed in several subsequent divisions of physics and a theory of the existence of a Higgs Boson component, said to be the “holy grail” of science as we know it. Perhaps the following on this topic, is a good example of how  Newtonian influence has empirically spanned science into the modern era. As recent as 2005, physicists along with a host of other scientists from around the globe began experiments at CERN Laboratories [9] already yieldeding promising results in the way of proving that there exists a quantum model/structure/form or as I like to call it “entity”  that gives weight to atomic particles, called a Z Boson. [10] Update: 2017 CERN: Higgs Particle

Newtons study of Pure Optics (See, Pure Mathematics) came to influence Applied Optics and other fields such as electrical engineering, Ophthalmology and even studies in psychology. [11]

Newtonian Influence on Mathematics

As I had mentioned in the section on optics, Newton had come to be influenced by the work of Johannes Kepler – possibly while he was studying Kepler’s geometric approach to optics and(or) theory of lenses as part of his mathematical studies at Cambridge. Kepler’s focus on the movements of celestial bodies as orbiting in elliptical motion led him to his postulation that planets orbit around the sun – heliocentricity. Kepler came to this idea by his recount with what had been studied by another astronomer prior to his time, Nicolaus Copernicus.
“This ultimately led to his work, the Laws of Planetary Motion which set in place the foundational premise of consideration for Newton in what would inspire his own discoveries about the laws of motion and theory of Universal Gravitation. This was also accomplished in part to the application of Euclidean geometry.” [8]

Isaac Newton’s 1687 scientific treatise, The Mathematical Principles of Natural Philosophy or in latin, Philosophiæ Naturalis Principia Mathematica, describes Newtonian Mechanics or as it is better known, Classical Mechanics, as the functions of application of physical properties to mathematical expressions for motion (i.e. velocity) that became Newton’s laws of motion. The Law’s of Motion were governed by three principle laws or scientific laws and there correlative properties. For example, a general property would be the Law of Approximations – as part of the Law’s of Motion. In relationship, “Several mathematical theorems and the contexts of those theorems as axioms and postulates, are governed and referred to by certain laws or rules because they provide logical foundations to empirical truths or empirical laws.” [12]

Newton’s Method of fluxions are based on differential calculus – and they are very similar to a mathematical study of functional relationships that would come to be defined by Albert Einstein’s Theory of Relativity (see below). Newton published his method of fluxions in The Mathematical Principles of Natural Philosophy (latin, Philosophiæ Naturalis Principia Mathematica) and Gottfried Wilhelm Leibniz, a german mathematician who had been in communication with Newton about these methods came to publish a paper on infinitesimals (infinite being a characteristic property of Newtons law’s of motion) called, the Calculus. This led to a historic dispute in which the outcome credits both men for the development of infinitesimal calculus. “In Isaac Newton’s universe there were three dimensions: length, breadth and width. These three dimensions could not be interpreted by elementary two dimensional Geometry, so Newton created calculus. [13] See, History of Mathematics – Central Controversies: Created or Discovered?

Newton also studied René DesCartes’ (the French Mathematician and Philosopher who coined the initially derogatory term, “imaginary numbers”) Lé Géométrie. By my own recount of the timeline here – DesCartes’ work had probably just been published in the universally scholastic language, Latin, whereby prior to this time, the paper remained in french. Note- Newton also wrote papers in Latin. At one point Newton actually “expressed his regret that he had not applied himself to geometry before proceeding to algebraic analysis.” [14] Despite the fact that he applied himself enough so that Calculus is based upon both Geometry and Algebra – which is why it is studied in sequence prior to studying Calculus.

Newtonian Mechanics & Gravitation Theory

Newtons Law’s of Motion were later built upon by Albert Einstein’s Theory of Relativity. The differences of Einsteinian versus Newtonian theory were developed in accordance with the eventually better understood properties of light. Newton believed that light was instantaneous in nature however, this was not true. As Newton used the term “duration” as a variable in describing the constant nature of matter in the physical universe and “light” as the source that reflected in particle mechanics (pun intended) including in relationship to gravitation (observed as a force that pushed and pulled objects into place) it appeared as a result thorough his experimentation- that light was in fact constant. Later on in mathematical application, light was proven to not be instantaneous but to move at a fast duration or rate. The speed of light constant is represented by c in E= Mc^2. Einstein did consider the similar aspects of Newtonian laws in so much as length, breadth and width as properties of universal mechanics however he collectively called these properties, “space” as interdependent to “time” as a whole of dimensions that were relative to one another and responsible for variabilities within a set of properties and behaviors. Rather then viewing time as a unit for measurement as Newton did, Einstein viewed it as a collective variable to other three-dimensional elements of space, governed by Velocity.  [13] See, Planck Time and Max Planck; Planck Constants.

Newton’s Gravity

Newton’s first Law of Motion is based on the establishment of the principle of inertia. Inertia applied to the state of force and motion acting on matter with respect to position manifests as velocity to mass relationships, qualifiable in equation form. Force is describe by a form of energy that may be described by the Second Law of Motion or the Law of Heat Conduction, or even the General Law of Gravitation. The law of Inertia is an empirical premise for the study of classical physics. [15] This influenced later advancements for Western Civilization in, for instance, that the concept of inertia as relevant to the studies and training of astronauts at the National Aeronautics and Space Administration (NASA). Newton’s Third Law of Motion stipulates that “For every action, there is an equal (in size) and opposite (in direction) reaction force.” [16] See the definitions of Magnitude and Direction; Vectors and Scalars.

Newtons Law of Heat Conduction also spurred several important developments including The theory of Relativistic Heat Conduction (RHC) which also pertains to the ideas of relativity as set forth by Einstein. (The theory of Relativistic Heat Conduction (RHC) having to do with the process of conductivity as “catalyzed” by heat or thermal energy.) The concept of diffusion is aggregated to Fick’s laws of diffusion which is analogous to the Law of Heat Conduction and defines a mechanism of synthesis and reaction founded by empirical processes.

Quantum Mechanics and Gravitation

Quantum Physics has adapted Newton’s Law’s of Motion and applied it to studies of the natural world in a concrete and absolute procedure that governs the modality of further exploration in this field of science. Even in consideration that that of Newtonian theory on light as it is understood in the Law’s of Motion -as an immovable constant source or instantaneous force- would be proven false in later scientific and mathematical applications- his work in proving the Principles of Gravitation remained accurate. Newton’s General Law of Gravitation explained the forces between objects as Gravitation (a sort of universal glue) and further that the force of Gravity is variable upon the dimensions of mass which included length, breadth and width (Newton) versus the division of space between each object, then squared (Einstein). The equation for the General Law of Gravitation (figure 1) had been revised in Einstein’s field equations which helped to develop more precise gravitational measurements. Note, Gravity was visually mapped for the first time in 2016.* See, Publications on Gravity by CalTech.

The exploration of material states and relativity to the force of gravitation, as well as other properties, opened doors for the study of micro-particles or very basic atomic and sub-atomic structures. Similarly, the behavior of subatomic structures under the influence of force and as vectors in space have continued to be studied by CERN Laboratories. However, CERN Laboratories has not conducted the only major research that has uncovered new truths about the functional aspects of quantum mechanics! A Physicist named Nicolas Gisin, one of two Swiss Physicists has very recently, within the past several months (2005) conducted an experiment with photons. In quantum mechanics, the two physicists who conducted the experiments including Gisin, observed a reaction between split photons that were sent 11 miles in opposing directions in “conduction” along fiber optic cables. Upon interaction and intentioned manipulation of one photon arriving in one directional position, the other, remaining a distance apart – changed instantaneously. You can see how some of what we know about Classical Mechanics “crumbles” at the Quantum level. The photons changed “state” alludes to evidence in support of quantum entanglement theories (Einstein). During this experiment, extreme rates of reaction were observed, the scale of which had to be measured in Planck time (~ 10-43 seconds). Relativity, in theory, tells us that it is not possible for this reaction to occur but the exception is where the absence of a communicative signal exists upon the incidence of reactive photons.” [18] Here in the above, you can see one of the most outstanding examples of how far reaching the affects of Newtonian influence have into the modern era.

FIGURE 1: General law of gravitation

The UNIT of measure employed by the initial methods of Sir Isaac Newton’s classical mechanics and used to measure gravitation and force therein is called a Newton, symbolized as N.
Newtonianism, as the coined term for Newtons theoretical influences, philosophies and methods, Newtonian Mechanics, Newtonian fluids, the newton (or N) as a unit of force ALL warranted new scientific units of measurement (i.e. the kilonewton) which are even applied in the field of Architecture.

Newtons practice as an Alchemist and Chemist

As Newton used colors to describe his earlier experiments with light, matter and optics, in more modern times, we look at similar characteristics of matter in the study of Chemistry!

Newton was an alchemist and a very spiritual man. I think that others have precluded, as do I, that this fact is centrally important and reflective in of all of his work in that his belief was in the existence of a more divine sense of order. Those beliefs ultimately led him to what he personally considered some of his most significant work. (See below)

Alchemy stems from the ancient civilizations of Mesopotamia, Egypt, Persia, India, Japan, Korea, China, Greece and Rome. [19]
The origins of alchemy had been so widespread during Newton’s time and its universally appealing presence existed beyond the boundaries of culture and time eventually leaning to intrinsic understanding and organizational discoveries of material chemistry. Alchemy refers to the investigation of the natural world from the perspectives and foundational premises of chemistry, physics, medicine, astrology, semiotics, mysticism, spiritualism and art as all parts of one greater force. [19]

In his approach of alchemy, Newton remained religious. Even so, the practice of Alchemy is not viewed by the church as orthodox and at one point in time during the Inquisition, those who practiced Alchemy would be considered heretics resulting in their being tortured and often martyred. This is why, around the same time, a famous astrologer and astronomer, healer and alchemist, Nostradamus encoded his quatrains of his Les Propheties or in english translation, The Prophecies.

In 1690, Newton began studying theological prophecies and “wrote in the form of a letter to Locke, a Historical Account of Two Notable Corruptions of the (Christian) Scriptures regarding two passages on the trinity, and he left in Manuscripts, Observations on the Prophecies of Daniel and the Apocalypse.” [1] It is said that Newton spent a considerable amount of time exploring biblical texts in the hopes of discovering a codex for hidden messages that he adamantly believed to be encoded in the bible. This work would be appreciated and undertaken by other scientists, scholars and alchemists in times to come. Overall, his work proved concrete and formidable but it is refreshing to find that his thoughts expanded a theoretical box and pushed the boundaries of what was accepted and understood- perhaps a secret component to his utter brilliance.

References
[1]
“Isaac Newton”

[2] “Lycos, Inc. ”Isaac Newton: Woolsthorpe Manor””
April 2008. 4 May 2009

[3]Huygens, Christiaan. Great Books of the Western World, vol. 34 Newton, Huygens. Chicago, London, Toronto, Geneva:Encyclopedia Britanica, Inc. 1952: ix-x.

[4]“British History: Scientific Revolution” “Scientific Revolution.” Encyclopedia of the Early Modern World. The Gale Group, Inc, 2004. Answers.com 24 Jun. 2009.
“Scientific Revolution.” A Dictionary of British History. Oxford University Press, 2001, 2004. Answers.com 24 Jun. 2009.

[5]“Natural philosophy”

[6]Opticks: Or, A Treatise of the Reflections, Refraction’s, Inflections and Colours of Light. The Second Edition, with Additions (London: 1717)1717, in English, c. 24,028 words, The Third Book of Opticks. Part I
Published in: Opticks: Or, A Treatise of the Reflections, Refraction’s, Inflections and Colours of Light,
Second Edition(London: 1717)

[7] ”Mr. Isaac Newtons Answer to some Considerations upon his Doctrine of Light and Colors”
printed in Numb. 80. of these Tracts 18 November 1672, English, c. 7,955 words, 20 pp. Published in: Philosophical Transactions of the Royal Society No. 88, pp. 5084-5103.)

[8]“Johannes Kepler”

[11]“Optics”

[12]“Physical law; Laws as Approximations”

[13] Webb Jr., John Charles ”Thought Faster then Light”
1997-2008. May 2009.
[14]D.R. Wilkins(dwilkins@maths.tcd.ie), School of Mathematics: Trinity College, Dublin “A Short Account of the History of Mathematics” (4th edition, 1908) by W. W. Rouse Ball.
May 2009.

[15] “Classical Physics”

23 June 2009. 4 May 2009.
[16] Henderson, Tom “The Physics Classroom Tutorial” 1996-2007. May 2009.
17] Ornes, Stephan “Top 100 Stories of 2008 #43: Next-Level Quantum Spookiness” Discover: Science, Technology, and The Future: Physics & Math; Light 14 December 2008. January 2009.
[18] Jovanovic, Radoslav B.Sc (Electrical Engineering) High School for Electrical Engineering, Lajkovac, Yugoslavia. “Golden Section: Fibonacci Numbers and the Pascal Triangle; Planck Constant and Number Pi” 2001-2007. November 2007. May 2009.
[19]“Alchemy”

Resources
Main Source: Newton, Sir Isaac. Philosophical Transactions of the Royal Society, No.80 (19 Feb. 1671/2), pp. 3075-3087. A Letter of Mr. Isaac Newton … containing his New Theory about Light and Colors
[9](http://public.web.cern.ch/public/)
[10]

Publications
Newtons publications in accordance with the following source:
“Sir Isaac Newton” Alfred Rupert Hall, Microsoft® Encarta®. 1998 Microsoft Corporation. Isaac Newton Institute for Mathematical Sciences “Isaac Newtons Life”, are as follows:
• An edition of Geographia generalis by the German geographer Varenius in 1672
• His own letters on optics appeared in print from 1672 to 1676.
• Principia (published in Latin in 1687; revised in 1713 and 1726; and translated into English in 1729).
• Opticks in 1704; a revised edition in Latin appeared in 1706.
• The Chronology of Ancient Kingdoms Amended (1728)
• The System of the World (1728)
• Book III of the Principia, and Observations upon the Prophecies of Daniel and the Apocalypse of St John (1733).

 

Federal Period Architecture: Exploring Neoclassical Influences on American Architecture (1785-1830)

 

Federal Period Architecture: Exploring Neoclassical Influences on American Architecture (1785-1830)

The Federal Period (1785-1830) in American architecture was characterized by the influence of Neoclassical design, which originated from ancient Greek and Roman architectural traditions. This article delves into the architectural aesthetic landscape of the Northern and Southern American colonies during this period, highlighting the key architects and design elements that shaped this era.

I. Classical Period and Architecture: Architecture, as an art form, has played a crucial role in shaping the landscape of early American public buildings and private residences. Looking back to the Classical Period, particularly ancient Greece and Rome, provides a deeper understanding of the Neoclassical influences observed in American architecture during the 17th and 18th centuries.

  1. Greece and Rome: The ruins and elements of classical architecture found in Greece and Rome served as the foundation for Neoclassical architecture in America. These ancient civilizations had a profound impact on the architectural style, as they encompassed physical constructions and philosophical symbolism. From roadways to colosseums and temples, these classical elements resonated with the Neoclassical movement in American design.
  2. Neoclassical Influence and Adaptation: The Neoclassical influence in America coincided with the adaptation of classical elements from their origins and their resurgence in foreign countries. Notably, the French architect who worked on Thomas Jefferson’s renowned estate, Monticello, incorporated some of these classical elements. The appeal of classical architecture extended beyond its visual aspects, as it symbolized the imperial and powerful ruling democracies of the Greco-Roman Empires, which resonated with the newly established American democracy.

II. Neo-Classicism: Neoclassicism, a revival of Classical themes and styles, gained prominence not only in America but also in various European countries. America embraced its own version of Neoclassicism, heavily influencing the architectural landscape of both the Northern and Southern colonies until the Romantic and Victorian styles emerged after the Civil War.

  1. Excavations and Discoveries: One significant catalyst for the Neoclassical movement in America was the exploratory excavations that unearthed artifacts of Classical Antiquity. The discoveries made in ancient Roman architectural ruins, such as Herculaneum and Pompeii, shed light on the architectural achievements of Classical societies. These findings fueled the transition to Neoclassicism, with the Adam style acting as a subtractive source of influence for America’s Federal Style.
  2. European Influence: Neoclassicism in America evolved from the broader European movements, particularly the Georgian style from France and England. The Neoclassical Federal Style, with its meaningful representations and appeal to American ideals and values, found its place in the architectural landscape. Public buildings, schools, churches, banks, and wealthy private residences reflected this style, showcasing its prevalence in both the Northern and Southern states.

III. The American Architects of Neoclassical: Federal Style: Several prominent architects played a crucial role in defining the Federal Style during the Neoclassical period. Their contributions significantly shaped the architectural landscape of America, and here are a few noteworthy architects and their achievements:

  1. Asher Benjamin: Considered a pioneering American architect, Asher Benjamin published books featuring Neoclassical designs and architectural sketches. His work influenced other architects and reflected the adamesque British flare of classical revival architectural style.
  2. Charles Bulfinch: Charles Bulfinch, the first American-born architect of the Neoclassical Federal Style, left a lasting impact on the architectural scene. Notably, he designed the rotunda and dome of the US Capitol building.
  1. James Hoban: James Hoban, an American Freemason of Irish origin, designed buildings across various states, leaving an indelible mark on the Neoclassical architecture of the Federal period. One of his most famous works is the White House, the iconic residence of the President of the United States. Hoban’s design for the White House was heavily influenced by classical Greek and Roman architecture, featuring a grand portico with Ionic columns and a central pediment.
  2. Benjamin Latrobe: Benjamin Latrobe, often referred to as the “Father of American Architecture,” made significant contributions to the development of Neoclassical architecture during the Federal period. He was appointed as the Surveyor of Public Buildings in the United States and was responsible for the design of important structures such as the United States Capitol’s south wing. Latrobe’s designs showcased a blend of Neoclassical elements and innovative engineering techniques, incorporating domes, porticos, and intricate detailing.
  3. William Thornton: William Thornton, a British-born architect, played a pivotal role in shaping the Federal period’s architectural landscape. He won the design competition for the United States Capitol building, and his plan served as the foundation for the iconic structure we see today. Thornton’s design incorporated Neoclassical features, including a grand dome and a central portico with Doric columns, reflecting the influences of ancient Roman and Greek architecture.
  4. Robert Mills: Robert Mills, an American architect and engineer, made significant contributions to Neoclassical architecture during the Federal period. His notable works include the Washington Monument, which stands as a towering tribute to America’s first president. Mills’ design for the monument embraced classical influences, featuring a tall obelisk structure reminiscent of ancient Egyptian architecture, topped with a Neoclassical-style statue of George Washington.
  5. Samuel McIntire: Samuel McIntire, a master woodcarver and architect, made significant contributions to the development of Neoclassical architecture in New England. Known for his exceptional craftsmanship, McIntire’s work incorporated intricate detailing and delicate ornamentation, reflecting the elegance and refinement of the Federal Style. His designs included private residences, public buildings, and decorative elements such as mantelpieces and carvings that became synonymous with the Federal period’s architectural aesthetic.

IV. Key Design Elements of Federal Style: The Neoclassical Federal Style of architecture encompassed several key design elements that set it apart from earlier architectural styles:

  1. Symmetry and Balance: Federal-style buildings were characterized by their symmetrical and balanced facades. The use of evenly spaced windows, doors, and ornamentation created a sense of harmony and order.
  2. Classical Motifs and Details: Architects incorporated classical motifs and details, such as columns, pediments, and entablatures, into their designs. These elements were inspired by ancient Greek and Roman architecture and added a sense of grandeur and authority to the buildings.
  3. Porticos and Entryways: Grand porticos with columns, often in the Ionic or Doric order, were a prominent feature of Federal-style buildings. These porticos served as entryways and provided a sense of welcome and importance.
  4. Palladian Windows: Palladian windows, named after the Italian architect Andrea Palladio, were another common feature of Federal-style architecture. These large, arched windows with smaller rectangular windows on either side added elegance and brought in ample natural light.
  5. Rooflines and Cornices: Rooflines in Federal-style buildings were typically low-pitched and often featured decorative cornices. The cornices added a touch of refinement and provided a transition between the walls and the roof.

The Federal period in American architecture, characterized by the prominent influence of Neoclassical design principles, stands as a significant chapter in the nation’s architectural history. During this era, a group of talented American architects, including James Hoban, Benjamin Latrobe, William Thornton, Robert Mills, and Samuel McIntire, emerged as key figures, leaving an indelible mark on the architectural landscape.

The Federal architects drew inspiration from the classical architectural traditions of ancient Greece and Rome, skillfully blending these influences with innovative engineering techniques and a distinct American sensibility. Their designs reflected the ideals of the newly formed nation, emphasizing order, symmetry, and elegance.

One of the most iconic examples of Federal architecture is the White House, designed by James Hoban. Its grand portico with Ionic columns and central pediment became an enduring symbol of presidential power and the nation itself. Benjamin Latrobe, revered as the “Father of American Architecture,” made significant contributions by infusing Neoclassical elements with inventive engineering, exemplified by his work on the United States Capitol.

William Thornton’s design for the Capitol, chosen through a design competition, established the foundation for the monumental structure that stands as a testament to democracy. Thornton’s inclusion of a grand dome and a central portico with Doric columns pays homage to the architectural heritage of ancient Greece and Rome.

Robert Mills contributed to the Federal period with his design of the Washington Monument, a soaring obelisk adorned with a Neoclassical-style statue of George Washington. Mills’ incorporation of classical influences and his masterful execution elevated the monument into a timeless symbol of the nation’s first president and the ideals he represented.

In New England, Samuel McIntire showcased his exceptional craftsmanship and artistry by blending intricate detailing and delicate ornamentation into the Federal architectural style. His work adorned private residences, public buildings, and decorative elements, embodying the refined elegance characteristic of the period.

Key design elements of Federal architecture included symmetrical and balanced facades, the incorporation of classical motifs and details such as columns and pediments, grand porticos with Ionic or Doric columns, the use of Palladian windows to bring in natural light, and the addition of decorative cornices to enhance the rooflines. These design elements created an architectural language that exuded a sense of harmony, authority, and refined aesthetics.

The enduring legacy of the Federal period in American architecture is seen in the many buildings and structures that still grace the nation’s cities and towns today. Its influence extended beyond the Federal era, laying the foundation for subsequent architectural styles and shaping the development of American architectural identity.

In conclusion, the American architects of the Neoclassical Federal Style made significant contributions to the architectural landscape, producing buildings of timeless beauty and embodying the ideals and aspirations of a young nation. Their designs, marked by symmetry, classical motifs, and refined detailing, continue to inspire and captivate, ensuring the enduring relevance of the Federal period in American architectural history.


Resources:

Kozlowski, M. (Photographer). Monticello [Photograph]. Retrieved from [insert URL]

Classical Period and Architecture:

Ancient Greece. (n.d.). Temple of Athena Nike. Ancient Greece: Architecture. Retrieved from http://ancient-greece.org/architecture/athena-nike.html

The American Architects of Neoclassical: Federal Style:

Monticello. (n.d.). Retrieved from http://www.monticello.org/

Palladian Style. (n.d.). Retrieved from http://www.boglewood.com/palladio/analysis.html

Virginia State Capital. (n.d.). The Library of Congress. Retrieved from [https://www.loc.gov/item/2018666788/]

The History of Mathematics: Coordinate Geometry vs. Non-Euclidean Geometry

Coordinate Geometry vs. Non-Euclidean Geometry

Coordinate Geometry:

During the time that Descartes (1596-1650) and Fermat (1601-1665) were developing their Mathematical Theories there were many Political and Cultural events occurring in Europe and the Americas. A great portion of Descartes life was lived out during the 17th Century AD (1601-1700) as well as Fermat’s, who was born at the turn of the century.

A movement referred to as the Baroque period in Europe began to dominate the cultural byproducts of Artistic endeavors. Partial to the movement were the wealthy class known as aristocrats that enjoyed the opulence and extravagance of Baroque values. The Baroque style and value not only could be found in Western painting but in the dramatic Arts, Literature, Philosophy, Sculpture, Clothing, Furniture, Architecture and Music as well. Patterns were reflected in Baroque styling.

In 1661, Louis XIV (1638 – 1715) assumed the throne of the French Monarchy as King of France, even though he had ascended the thrown at the age of 4. He was culturally known as an egocentric King, arrogantly relating himself to the likenesses of mythological gods. Under his political rule, Feudalism was disregarded and central government established. France was a power force amongst other European Countries at the time.

The Franco-Dutch War, and the War of the Spanish Secession found France at the forefront.

The Scientific Revolution was spurring much scientific investigation- discovery and/or invention- throughout the Western world. At first this predominantly influenced European Cultures prior to spreading to the Americas. It encompasses that of great cultural advancement as science had become an enriching, empowering and notable force. Each progression marked a step toward modern science as we know it. Galileo Galilei left his mark on culture during this time, with his accomplishments in Astronomy and the physicist, mathematician, astronomer, alchemist, and philosopher Sir Isaac lived during this time.

In 1642-1649 a Civil War breaks out in England.

In the Americas, the pilgrims arrive on the Mayflower ship, at Plymouth Rock in 1620. Soon after many English settlers began to colonize the America. In 1622, the Jamestown Massacre was marked by eastern native Americans killing hundreds of English that lived in the colony of Jamestown. A great cultural achievement in the Americas during the 17th century was the founding Harvard University.

Non-Euclidean Geometry:

During the 16th, 17th, 18th, and 19th centuries there were many developments that played a role in the “Scientific Revolution.”

Riemann – German 1826-1866

Germany as a Holy Roman Empire

Immigration by Germans to the United States of America occurred during this time period and the Scientific Revolution was continued in the United States during this time by people such as Thomas Jefferson.

Industrial Revolution

1866 Austro-Prussian War: Prussia overcomes leader Otto Van Bismark

Lobachevsky – Russian 1792-1856

Russia in the 1800’s was under the rule of a Czar (similar to a King). Post social and political Revolution was a time when the Russian people remained oppressed which lead to civil war and eventually influenced the future development of the Soviet Union and communist control.

Workers guilds against post-industrial revolutions factory building

Bolyai – Hungarian 1802-1860

Hungary in the 19th century saw social changes in population class status’ and the nationality of hungarian nationals evolving with the population expansion that peaked in the 1800’s. The Upper class “Magnates” held positions of great power and influence over social political movement. They did not like the idea of the modernization because of its tie to population growth in the more diverse and lower class systems. The Industrial Revolution and modernization caused the hungarian magnates to reach out to Vienna, the Austrian capital for an alliance in bringing about post-modernization social and political structuring dynamics.

Marine Biology: Morphological Change in Model Organisms- Student Blogger Example

Sample Article Review of Scientific Literature for Student Contributors to our Blog: Thoughts on Newton Blvd

Assignments for College Preparatory Science Students
by Academic Tutors 101

Subject: Marine Biology: Morphological Change in Model Organisms (Coral)

Citation: Todd, P.A. et al. An aquarium experiment for identifying the physical factors inducing morphological change in two massive scleractinian corals. Journal of Experimental Marine Biology and Ecology. 299 (2004): 97-113.

Source: This article was obtained through the Science Direct database at the www.esc.edu/library. (Note: Use “Export Citation” with the “ASCII” option to obtain the URL, then add “http://library.esc.edu/login?url=” in front of the “http” address. This will give you a stable link to the article.)

Note: You must supply the full and correct citation and whenever possible, a copy of a hotlink to the article itself. Your readers and students will want to read the actual article along with your review.

Summation: Prior research has shown that some species of coral are phenotypically plastic, but no controlled experiments had yet been done in a laboratory setting to try to determine the role of different environmental factors in facilitating morphological change. Researchers collected fragments of coral from different species of coral and grew them in different aquaria designed to represent varied light intensity, sedimentation rates and water current strengths. The corals were analyzed for morphological changes after 4 months of controlled growing experiments. They concluded that the most consistent morphological change seemed to be in response to light intensity.

Original source: Scientists from Scotland, Singapore, and Japan carried out this research at the Raffles Marina Research Station off the coast of Singapore.

What was studied: Fragments of different coral species were sampled during controlled laboratory experiments designed to distinguish phenotypic changes due to one or several environmental factors. Since the fragments were from the same coral colony, they were genetic clones of each other and therefore had the same genotype. Change in response to an environmental factor could then be known to be due to a change in phenotype. This is the coral equivalent of twin studies in Biology and psychology.

How the study was conducted: The control aspect in this study was attempted by leaving clonal fragments under natural conditions so as to have a comparison of any natural change in morphology over time. Many of these fragments were lost at sea and this highlights a difficult problem that often occurs in Marine Biology field studies!

What was concluded: They concluded that the most consistent change in morphology was the result of light intensity.

New questions: Corals seem to be very affected by environmental stresses. The paper mentions concerns about increased sedimentation and about climate change caused by global warming effects. It would be interesting to include water temperature as an environmental feature studied in the aquaria.

My opinion: After 4 months, the aquarium pump broke down and the study was prematurely ended. It is interesting to see that as long as a study is well-designed, something positive can be learned from it even when it doesn’t go as planned. In this case, the scientists learned more about the practical aspects of running the study, but also arrived at the conclusion to focus on light as a prime mover of phenotypic response.

This paper also highlights how little is known about coral biology, the roles, triggers, and biology of phenotypic plasticity in coral. There is also not much known yet about the ecology of phenotypic plasticity. This paper mentions that corals that are plastic are thought to be generalists. However, the cost and benefits of this trait are not yet clear in terms of evolutionary success and role in the community.

Glossary
*Be sure to use the college resources when building your glossary.

Genotype: Genotype refers to the genetic make-up of individuals and organisms. See Genetics.
This is a very important word in this article. Because the coral fragments were genotypically the same, the researchers were able to reason that any differences they saw in the individuals were a phenotypic adaptation to the environmental conditions.

Phenotypically plastic: Plastic means adaptable or malleable. See the Merriam-Webster dictionary. This concept is very important for understanding this study. With the same genotype, organisms showed different phenotypes under different environmental conditions. A phenotype refers to the physical result of a certain genotype. See Genetics.

How to Start Applying to College in New York State in 5 simple steps!

How to Start Applying to College in New York State in 5 simple steps!

REMINDER...

Take note of all submission deadlines for the academic year in which you wish to apply to College, on ALL forms. Some SUNY School’s have separate application deadlines.

1. Submitting your Application

You have some options, the Common Application or The SUNY Application? Which is best for you? Do you want to go to College in a State other then New York? If so, you will follow some different steps then those outlined here. Also, see the CUNY Application.

The Common Application

The SUNY Application

The CUNY Application

2. Qualifying for Financial Aid

To qualify for financial aid at the institution(s) of choice, you must complete and submit the free application for Federal Student Aid (FAFSA)

Note, you can and should list multiple Colleges and Universities even if you are waiting on some admission letters at the time of your FAFSA submission.

After submitting your FAFSA, you will be redirected to the Higher Education Services Corporation to file a separate application for NYS based financial aid programs like the new Excelsior Scholarship.

Types of Financial Aid

3. The Admissions Essay
You should search for Tips on How to Write your Admissions essay on the websites of the colleges and universities that you are applying to. You should consider what they are looking for and if you should apply using the SUNY Common App you will want to be inclusive of the criteria set forth by the institution(s) you are interested in as you respond primarily to the Common Application Essay Prompt of your choice.

2017-2018 Essay Prompts

4. Follow up with and check your Financial aid status about a month after submitting your FAFSA application. Make sure that there are no additional documents required by FAFSA and/or by the colleges you have applied to that will be receiving your financial aid information. (I.e., tax returns)

5. Await your acceptance letters!

Deadlines:
FAFSA

The Common Application

The SUNY Application (Pg. 4)

The CUNY Application

HESC Applications (SUNY & CUNY)

Evolution and Disease: Exploring the effects of Pathogenesis as a factor driving Natural Selection

Author: Lauren Feist

Affiliation: SUNY Stony Brook University

Publication Year: 2023 (Revised edition)

Title: Pathogens, Evolution, and the Role of Viral Pathogens: Insights into Genetic Variation, Disease Processes, and Evolutionary Change

Abstract:

Pathogens, including viruses, play a significant role in shaping genetic composition and driving evolutionary processes within populations. Through various mechanisms, pathogens introduce genetic mutations into host genomes, leading to new genomic and epigenetic effects. These mutations can contribute to natural selection by conferring advantages or disadvantages in survival and reproduction. The study of pathogenesis and evolution requires collaboration among different scientific disciplines, such as genetics, virology, biology, and chemistry.

By analyzing the genomic composition of infective agents, researchers gain insights into the relationships between pathogens and hosts, as well as the impact of these interactions on evolutionary change. Understanding how pathogens influence genetic variation, frequencies, and mutations provides valuable information about disease processes and the conservation of specific traits. The field of proteogenomics, which combines proteomics and genomics, allows for the exploration of protein structure, function, and expression in relation to genetic variations.

Sequencing entire genomes has revolutionized genetics, providing valuable insights into gene structure and function. Proteomic techniques and the study of post-translational modifications offer new avenues to explore the functions of proteins and their interactions with the genome and epigenome. Mapping protein form and function contributes to a better understanding of disease processes and the development of disease prevention and treatment strategies.
The evolution of pathogens, including antibiotic and disease resistance, is an important area of study within evolutionary development. Pathogens exert selection pressures on populations, leading to the survival and reproduction of resistant variants. Understanding the mechanisms and implications of antibiotic resistance is crucial for developing effective strategies to combat evolving pathogens.

The Borna virus serves as an illustrative example of an endogenous non-retroviral RNA virus. It replicates within human hosts, infiltrating the cell nucleus and transmitting through germ cells. The viral information is distributed within the genomic structure of subsequent generations, influencing gene expression through various mechanisms. The integration of viral genetic material into the host genome raises questions about its potential epigenetic effects and its role in human behavior and mental illnesses.

Further exploration of the human genome and mammal genomes reveals a greater viral component than previously recognized, indicating the existence of fossil viruses with implications for disease understanding and treatment. Viral pathogens, as non-living vectors, uniquely influence their own evolutionary trajectory by invading host organisms. The study of viral pathogens expands our understanding of evolutionary change and selection in living organisms.
Viral evolution can occur within host cells as well as through transmission between different host species, emphasizing the importance of tracking and projecting the evolution of pathogens for effective interventions. Integrating knowledge of viral integration, tumorigenesis, and core transcriptional features associated with neoplastic transformations provides insights into selection pressures, mutagenic changes, and mortalities in global populations. Understanding these mechanisms is crucial for the development of efficient disease management and prevention strategies.

The study of pathogenic populations and their role in evolution provides valuable insights into disease processes, genetic variation, and natural selection. By exploring genomic composition, mutations, and protein functions, researchers unravel the complex relationship between pathogens, hosts, and evolutionary change. This interdisciplinary field of research enhances our understanding of disease prevention, treatment strategies, and the broader implications of evolution in medical sciences.

Overall, this interdisciplinary research field, ( “Evo-Devo Pathogenetics”) contributes to our understanding of disease processes, genetic variation, and natural selection. The exploration of pathogenic populations and their role in evolution has far-reaching implications for disease prevention, treatment strategies, and the broader understanding of evolution in the medical sciences.

Keywords: pathogenesis, evolution, genes, pathogens, genetic variation, proteogenomics, antibiotic resistance.


Here is an expanded section with additional information and a chart highlighting the genes that are potentially involved in the processes described:

Pathogens, including viruses, play a significant role in shaping the genetic composition of populations and driving evolutionary processes. They introduce genetic mutations through various mechanisms, such as integrating their genetic material into the host genome, leading to new genomic and epigenetic effects. These mutations can contribute to natural selection by conferring advantages or disadvantages in survival and reproduction.

The study of pathogenesis and evolution requires collaboration among different scientific disciplines, including genetics, virology, biology, and chemistry. By analyzing the genomic composition of infective agents, researchers can gain insights into the relationships between pathogens and their hosts, as well as the impact of these interactions on evolutionary change. Understanding how pathogens influence genetic variation, frequencies, and mutations provides valuable information about disease processes and the conservation of specific traits.

Mutations, which can arise spontaneously or be caused by mutagenic factors, are essential for evolution by natural selection. They contribute to the diversity and polymorphic variances within populations and can be inherited through reproduction. Studying mutations and their effects on gene function and protein production deepens our understanding of the genetic basis of diseases and complex traits. The field of proteogenomics, which combines proteomics and genomics, allows for the exploration of protein structure, function, and expression in relation to genetic variations.

Sequencing entire genomes has been a groundbreaking advancement in genetics, providing insights into the structure and function of genes. Proteomic techniques and the study of post-translational modifications offer new avenues to explore the functions of proteins and their interactions with the genome and epigenome. By mapping the form and function of proteins, researchers can gain a better understanding of disease processes and potentially develop strategies for disease prevention and treatment.

The evolution of pathogens, including antibiotic and disease resistance, is an important area of study within the context of evolutionary development. Pathogens exert selection pressures on populations, leading to the survival and reproduction of resistant variants. Understanding the mechanisms and implications of antibiotic resistance is crucial for developing effective strategies to combat evolving pathogens.

The study of pathogenic populations and their role in evolution provides valuable insights into disease processes, genetic variation, and natural selection. By exploring the genomic composition, mutations, and protein functions, researchers can unravel the complex relationship between pathogens, hosts, and evolutionary change. This interdisciplinary field of research has the potential to enhance our understanding of disease prevention, treatment strategies, and the broader implications of evolution in the medical sciences.

Now, let’s chart some of the genes that are potentially involved in these processes:

Gene Name Function
p53 Tumor suppressor gene, regulates cell cycle and apoptosis
E6 Oncogenic protein of Human Papillomavirus
E7 Oncogenic protein of Human Papillomavirus
LINE Long Interspersed Repetitive Elements
URR Upstream Regulatory Region of HPV
H1N1 Influenza virus strain
HIV Human Immunodeficiency Virus
Various oncogenes and tumor suppressor genes Involved in neoplastic transformation and progression

Please note that this is not an exhaustive list, and there are numerous other genes and genetic elements that play significant roles in pathogenesis, evolution, and disease processes. The specific genes involved can vary depending on the pathogen and the host species under study.

 



Pathogens, including viruses, play a significant role in shaping the genetic composition of populations and driving evolutionary processes. Pathogens can introduce genetic mutations through various mechanisms, such as integrating their genetic material into the host genome, leading to new genomic and epigenetic effects. These mutations, in turn, can contribute to natural selection by conferring advantages or disadvantages in survival and reproduction.
The study of pathogenesis and evolution requires collaboration among different scientific disciplines, including genetics, virology, biology, and chemistry. By analyzing the genomic composition of infective agents, researchers can gain insights into the relationships between pathogens and their hosts, as well as the impact of these interactions on evolutionary change. Understanding how pathogens influence genetic variation, frequencies, and mutations can provide valuable information about disease processes and the conservation of specific traits.

Mutations, which can arise spontaneously or be caused by mutagenic factors, are essential for evolution by natural selection. Mutations can be inherited through reproduction, and they contribute to the diversity and polymorphic variances within populations. By studying mutations and their effects on gene function and protein production, researchers can gain a deeper understanding of the genetic basis of diseases and complex traits. The field of proteogenomics, which combines proteomics and genomics, allows for the exploration of protein structure, function, and expression in relation to genetic variations.

Sequencing entire genomes has been a groundbreaking advancement in genetics and has provided valuable insights into the structure and function of genes. The ongoing development of proteomic techniques and the study of post-translational modifications offer new avenues to explore the functions of proteins and their interactions with the genome and epigenome. By mapping the form and function of proteins, researchers can gain a better understanding of disease processes and potentially develop strategies for disease prevention and treatment.

The evolution of pathogens, including antibiotic and disease resistance, is an important area of study within the context of evolutionary development. Pathogens can exert selection pressures on populations, leading to the survival and reproduction of resistant variants. This phenomenon can be likened to predators and prey, where antibiotics act as the predator, killing some bacteria while allowing resistant variants to survive and proliferate. Understanding the mechanisms and implications of antibiotic resistance is crucial for developing effective strategies to combat evolving pathogens.

The study of pathogenic populations and their role in evolution provides valuable insights into disease processes, genetic variation, and natural selection. By exploring the genomic composition, mutations, and protein functions, researchers can unravel the complex relationship between pathogens, hosts, and evolutionary change. This interdisciplinary field of research has the potential to enhance our understanding of disease prevention, treatment strategies, and the broader implications of evolution in the medical sciences.

The Borna virus serves as an illustrative example of an endogenous non-retroviral RNA virus. Endogenous viruses originate within the tissues, organisms, or cells themselves and can impact the genetic makeup and functioning of the host. Empirical evidence suggests that the Borna virus is capable of replicating within human hosts by infiltrating the cell nucleus and subsequently transmitting through germ cells such as spermatozoa and oocytes. During gametogenesis, when germ cells from progenitor species merge, the viral information is often distributed within the genomic structure, specifically the chromosomes, of subsequent generations. The offspring’s genome becomes influenced by the provirus, which is the latent or concealed derivative of the Borna virus that has successfully integrated into the genomic structure. This integration occurs in regions where reverse transcriptase activity takes place or is encoded in Long Interspersed Repetitive Elements (LINE) or Long Interspersed Nuclear Elements (LINE).

It is plausible to speculate that this process could potentially trigger an epigenetic effect within certain loci of gene expression, leading to various outcomes such as epigenetic silencing, linkage, epistasis, null effects, or deletion mutations. In addition to these conjectures, the Borna virus has been identified as “replacing” the function of reverse transcriptase activity along LINE-1, where DNA copies of RNA are synthesized and inserted into the genome. Over generations, the viral DNA undergoes mutations, eventually losing its ability to mutate and becoming disabled.

Considering the aforementioned, one might question whether these viral remnants act as mediators of susceptibility to other viruses through overlapping protein sequences in a domain. In fact, an inverse relationship of this nature appears conceivable when examining the research of Dr. Keizo Tomonaga, a virologist at Osaka University, who fortuitously discovered that four segments of human DNA share clear ancestry with the Borna virus. Dr. Tomonaga’s theory proposes that the Borna virus did not invade mammalian genomes but rather that the genomes “kidnapped” the viruses, suggesting a synergistic relationship between human and viral genes. He suggests that LINEs, which have the ability to create copies of themselves, captured genes from the Borna virus and reintegrated them back into the genome. If this hypothesis holds true, it is possible that LINEs have also acquired genes from other viruses and utilized genetic material from those viruses in advantageous ways.

In his article “Hunting Fossil Viruses in Human DNA” (2010), Carl Zimmer mentions that the neurotropic Borna virus is just one of many viruses that infect mammals and birds. It is worth noting that birds, insects, and humans share a unique relationship, as vectors like mosquitoes are known to transmit viruses across species boundaries. Consequently, the presence of the Borna virus in various species is not surprising. Zimmer further explains that some species infected with this virus exhibit no symptoms, thereby rendering the effects of the infectious agent largely enigmatic, with specific exceptions. For instance, horses have been observed to display behavioral effects, such as wild fits that may lead to self-inflicted fatal injuries or starvation. Researchers have postulated a correlation between the Borna virus and human behaviors indicative of disorders such as schizophrenia. However, when considering the recent identification of protozoa affecting human behaviors and their role as pathogens or parasites underlying disorders like schizophrenia, we may gain further insight into the influence of pathogenesis on behaviors. The idea that pathogenesis can contribute to mental illness or influence behavior remains a topic of controversy, analogous to the initial debates surrounding the proposition of humans descending from primates. Anticipating a potential controversy over the notion that humans have limited control over their behaviors, the identification of pathogens responsible for behavioral influences could pave the way for targeted interventions and potentially lead to cures for various mental illnesses.
An alarming hypothesis, should it be considered conclusive, suggests that around 40 million years ago, the Borna virus infected our primate-like ancestors. Viruses are estimated to be present in approximately 8% of the genome in every individual on Earth, primarily in the form of endogenous non-retroviral RNA virus elements in mammalian genomes. To put this percentage into perspective, it is seven times greater than the DNA content of all the 20,000 protein-coding genes in the human genome. The completion of the human genome sequencing in 2001 revealed that several segments of human genes bear resemblance to retroviral genes. While scientists have identified connections between approximately 100,000 viral elements, mostly originating from retroviral infections, imprinted within the human genome, the discovery of the Borna virus as a component of the human genome represents a novel finding. This suggests that many other viruses may still await discovery within the human genome. Consider the implications of unraveling the form and function associated with these viruses—what other insights could be gained about known or unidentified diseases and their potential treatments?

The Borna virus is not the sole instance of fossil viruses revealed through gene mapping and referencing databases containing human genome sequences. Researchers are expanding their scope beyond the human genome and capitalizing on the growing number of mammal genomes available in online databases to elucidate the evolutionary history of viruses dating back millions of years. Collectively, these investigations provide compelling evidence that humans and other species have a greater viral component than previously recognized.
Of all the various pathogens I will discuss, viral pathogens, or “pathogenes” as I prefer to refer to them, hold particular significance. Unlike other pathogenic agents such as prokaryotes, archaea, and protozoa, viruses are technical, non-living vectors. Viruses uniquely possess genetic material that is not alive per se, requiring invasion of host organisms for survival and replication, thereby influencing their own evolutionary trajectory. The optimal conditions for viral evolution often arise when the host organism is not exploited to the point of death, ensuring the virus’s survival and reproduction in greater numbers. This concept theoretically applies to viruses, as it serves as the foundation for evolution through natural selection in living organisms. However, it is also plausible that certain viral pathogens may evolve by exploiting a host to the point of fatality while concurrently being transmitted to another host, facilitating evolutionary changes in both the host and viral populations. Viruses may evolve as they multiply within cells and reproduce. Is there a limited advantage, yet an advantage nonetheless, for viral pathogens gained by integrating into the host genome either during active infection or afterward as proviruses that are inherited by subsequent generations, thereby preventing their complete obsolescence? In my view, the answer is likely affirmative. This driving force of evolution is not limited to humans and animals but may extend to interactions between prokaryotes, archaea, and protozoa—what I term the “pathogen-to-pathogen route.” For example, eubacteria may be exploited by a viral population, presenting a symbiotic advantage in both populations. When examining the relationships between eukaryotes, prokaryotes, and archaea, we should explore a pathogenic phylogeny encompassing all domains and subsequent taxonomies.
Oncoviruses, which promote tumorigenesis in humans and animals, represent another extensively researched topic that expands our understanding of how viral pathogens can drive evolutionary change or at least fulfill the criteria necessary for selection to occur.

Interfering with the action of p53 allows a virus-infected cell to progress into a different stage of the cell cycle, promoting replication of the virus genome. Forcing the cell into the S phase of the cell cycle can potentially lead to cellular transformation (Scheffner et al., 1990).

According to a study conducted by the National Cancer Institute, HPV 16 is the most common type, accounting for 61% of cervical cancers, followed by HPV 18 at 9%. Types 33, 45, 58, and 59 were each found in one specimen. Analysis of the genomic sequences of HPV 16-positive isolates revealed distinct patterns of stability and variability in the upstream regulatory region (URR) and the E6 and E7 genes. Mutations were observed in 5% of the URR, including a large deletion in one isolate and various point mutations affecting regulatory sites. More sequence variations were found in the E6 gene compared to the E7 gene. Mutations in these genes, which encode the oncogenic proteins essential for malignant transformation, may impact the oncogenicity of the virus by altering amino acid sequences or transcription factor binding sites (Human Papillomaviruses and Cancer, National Cancer Institute, 2008; Int. J. Cancer 86:695-701, 2000).

Furthermore, it has been observed that viral evolution can occur not only within host cells but also through transmission between different host species. Examples include the H1N1 influenza virus, which originated in swine populations and crossed the species barrier to infect humans, as well as avian influenza viruses undergoing multi-species crossing-over.

In terms of gene expression and profiling, a large-scale meta-analysis of cancer microarray data revealed common transcriptional profiles associated with neoplastic transformation and progression. This analysis examined 40 published cancer microarray datasets, encompassing over 3,700 cancer samples and 38 million gene expression measurements. The findings indicated a common transcriptional profile in various forms of undifferentiated cancers, suggesting core transcriptional features associated with neoplastic transformations and the perpetuation of cancer development (source: Large-scale meta-analysis of cancer microarray data identifies common transcriptional profiles of neoplastic transformation and progression).

These findings highlight the significance of viral integration within the human genome and its role in driving evolutionary changes, with tumorigenesis being one measurable outcome. Understanding these mechanisms is crucial in medical science, as it provides insights into selection pressures, mutagenic changes, and mortalities in global populations. By comprehending the evolutionary aspects, research can be directed towards developing effective treatments and prevention strategies. Targeting the most virulent strains of pathogens while minimizing harm to the host appears to be a promising approach for disease management and prevention of resistance. However, in the case of HIV, all variants of the virus exploit the host in harmful ways, posing challenges for this approach. Thus, closely tracking and projecting the evolution of pathogens is crucial for the development of efficient interventions.


Citations

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