How math in science is different from math in math.
In order to better understand the role of math in sciences, what are some examples of modern day
physical systems that are modeled using equations?
Can we write something that makes physical sense but is mathematical nonsense?
Are there any differences in graph data interpretation from the math in science and the math in math to
find relationships and patterns from a set of data
I remember in high school, every math class I took always focused on "real life" word problems where we
had to apply what we learned. However in MATH141 there was very little of this. Is this a longstanding
trend or a recent one?
When we are going to learn a topic in math or physics to understand science, will we be using broad or
specific biological examples?
What is considered semi-quantitative reasoning and how can you differentiate it from regular quantitative
reasoning? Is it even relevant to do so?
Reason #5 states "the same symbol will sometimes be used for an independent variable or a dependent
variable." In what types of situations would the same symbol be used for both variables, and how is one
able to differentiate between the variables if the same symbol is used?
It is said that we use equations to model a physical system. In what ways will we be doing so? Also, will
we just be modeling the system, or both modeling and solving?
Is there any way we could use math with more conceptual ideas such as evolution and natural selection?
Also could that be the reason evolution is still a theory because they have not been able to prove it using
math therefore showing its consistency?
In regard to points 1 and 4, is the only difference between pure numbers and numbers with units that you
need to make sure you never try to equate two quantities if their units or different, or are there other
implications of numbers coming with units in the physical sciences
How do you account for the variability of biological communities? For example, if you were calculating the
carrying capacity of a population, how could you use an equation to account for sickness or a lack of
predators?
It was mentioned that symbols in science can be used as constants or variables interchangeably. The
example that was given was concerning mass - my question is, in what type of experiments is mass used
as a constant and when is it used as a variable? I am having a difficult time understanding where the
change occurs.
How can the structure of an equation be used to newly conceptualize the system that the equation is
being used on
How likely is it that will we find mathematical homonyms in a given problem in this course?
I understand that there is a difference between "math in math" and "math in science", but how can we use
math or numbers to model science and have it make sense?
Why don't they try to differentiate variables of the same kind in math in science? For example, if a
problem has two "T" variables (one for tension force and one for time) then why not label the tension force
variable as "Tf" and the time variable as "Ti"?
In point number 7, it states that sometimes the same symbol can be used to represent two different things
in the same problem. When would this be beneficial to use and what is an example where this is seen?
If we were taught to just solve for variables in introductory math, how do we learn to think about the
physical meaning?
If variables and constants are plastic in relation to a specific model as it relates to a natural science
scenario, can a research paper use novel symbols in order represent newly discovered or derived
variables/elements/constants?
What happens when pure math cannot explain your findings in an experiment? At that point, would that
mean that I should stop using math, and look for a different approach?
It seems that math in science does not always give you an absolute answer because it's used to model a
physical system. So, how do scientists know whether or not their answers are correct if the answer could
be different every time?
What are some benefits that quantitative modelling has over qualitative modelling?
By the third point, "The symbols in science classes often carry meaning that changes the way we interpret
the quantity", do you think that a good example would be when we have to pay attention to whether delta
G is negative or positive, indicating whether it is spontaneous or not? I'm assuming that is what you mean
by how we interpret the quantity.
How can certain unitless constants like pi be applicable to so many situations in science?
In math classes we are often prompted to solve for something. The article mentions how usually multiple
symbols are used in a single equation; is it common to not solve for one particular thing at a given time in
physics?
The article states that math in science requires one to identify what equation to use, which is a factor that
distinguishes it from pure math. However, could this factor also apply to pure math as well--like choosing
the correct equation to find the slope of a line or a derivative?
"We shouldn't use the same symbol to have different meanings in the same problem, though sometimes it
happens." Based off of this statement from the text, how would the same symbol have different meanings
in the same problem? a
I have always struggled with distinguishing between constants and variables. My question is what is the
difference between a constant and a variable and how are different constants determined? Are formulas
and equations also used to measure a constant?
For equations modeling systems, is it more important to recognize the relative trends than do exact
calculations
Based on point #6, how can one draw qualitative conclusions about a physical system from the structure
of a mathematical equation? What does one analyze to draw these conclusions?
For the seventh reason, it says "We shouldn't use the same symbol to have different meanings in the
same problem, though sometimes it happens." What is an example in which this occurs? On an exam, in
order to make things easier for our work, are we allowed to substitute symbols? For example, if there are
two quantities for which the variable "m" is used, are we allowed to write on the exam "the m representing
_____ is going to equal n for the purposes of this problem" that way we don't mix up variables?
Why is mathematics culturally taught as a computational tool instead of as a means to fundamentally
model reality?
What is good way to start being able to recognize the physical meaning hidden inside math problems?
How are equations conceived for use in a scientific setting and how are they verified? In other words are
they derived from experimentation and then tested in other situations, are they conceived through
brainstorming and then tested on an experiment, or is it a little of both?
Rather than using a large set of variables and constants for physics equations, can this notation be
simplified to resemble basic math in math classes?
As mentioned in the reading, sometimes "the same symbol has different meanings when the context
changes". This proposes a difficulty when solving a problem that requires the usage of a symbol that may
mean two different things. For instance, a problem may ask to quantify tension along with a period of
time, which both are represented by "T". How can a scientist account for "mathematical homonyms" in
his/her calculations? Are there existing equations that include two different variables represented by the
same letter?
The reading says that we are not using numbers, but physical qualities expressed as numbers via
measurement. Does this mean that science in math is only considered "modeling" if it uses real data from
experiments, rather than hypothetical values?
You say that, in science, different kinds of quantities cannot be equated to each other, but aren't there
situations in science where different kinds of quantities CAN be equated to each other? For example,
couldn't someone use information about the pressure and volume of a gas in order to equate to the
number of moles of that gas?
My question is, how do scientists feel about the use of theoretical estimations methods that
mathematicians use to estimate equations to simulate real life models?
What are specific examples of situations that model real world chemical, biological, or physical systems in
which a symbol generally used as a constant would shift from being a constant to variable? Additionally in
those examples why, specifically, do these symbols change in this manner?
Can you give an example of how you can "learn new conceptual ideas about the physical system being
described from the structure of an equation"? I am struggling to come up with an example on my own.
In an effort to simplify the understanding of mathematical models, wouldn't it be less confusing to use
different symbols (instead of only using k for example), to represent different constants?
To remember the symbols in equations, is it a good idea to use units to help?
How much math are we doing for this course?
Even though math in science mostly consists of unsolvable equations, how do biologists, chemists,
and/or physicists reach valid quantitative evidence and data?
As in reason 7, what should we do when we have same symbols and a different context in the same
problem?
Reason 5 discusses how symbols may shift from constant to variable depending on the situation, but how
will we know what to look for to know which to use and when?
Pertaining to Reason 4: if different kinds quantities can't be added or equated, how would one explain
relationships such as PV=nRT, a gas law, which equates different types of quantities together?
Is math used to model physical systems in subjects other than science? if yes, how so?
How do we train ourselves to see math as a tool for physical models rather than tools for calculations?
Why do physics equations have more symbols than a typical calculus equation? And if they don't follow
the math convention, how will we solve these problems?
Why is it that in mathematical math there is a solid limit for the amount of symbols used while in scientific
math there is not? Wouldn't this just cause confusion in the variables you are actually trying to solve for?
Even though there are all these differences, will we still need to have knowledge of advanced concepts
taught in upper level math courses? Or will we be mainly using more basic common concepts?
How do equations in pure math exist if they make no physical sense?
You said we have to be careful not to write something that "makes mathematical sense but is physical
nonsense" - can you give an example of this?
When using mathematical models to interpret/represent physical systems, how do these models account
for changes in the physical environment surrounding the system (do the models we use operate under
the assumption of a closed or open system)?
In the web page, it is said that many symbols we use shift meanings (what they represent). What is an
effective way to distinguish/discern when the meaning of the symbols shift? Also, what is the difference
between dependent and independent variable?
I understand that math in science is used as a model rather then a calculation, however, how would we
design a model to illustrate a given phenomenon. For instance, how would one calculate the diffusion rate
of air across the alveoli, would one first need to gather data and what is the start point?
A symbol is typically used as a representation of one singular idea and it is constant, so why is it altered
based on the context and doesn't that impede on our ability to reference a symbol and assume that it will
be understood in any context?
How do you make a model using math for a biological system that is based on random motion?
For example - substrates and enzymes meet and join due to random motion and chance, can that be
modeled using math?
Thus, by thoroughly understanding the use of math in physics, would we learn to apply it to science (ie.
the extension which an arm can stretch/bend until the action becomes destructive to the overall physical
state of the arm), or at least get a concept about it?
If units are so important, why are they not used in most of the math that we have been taught so far in
college?
Throughout the article its repeated that "math in science is NOT math as a calculational tool, but as a way
to represent information," but aren't scientists attempting to calculate something? I kept thinking of how
we used equations in BSCI106 to calculate population density, growth rates,etc. I don't understand how
it's not a calculational tool if we're using it to eventually using it determine a value.
Why does math use the conventions for variables, functions and constants, but physics does not?
Wouldn't it make sense to use the same conventions in every academic subject?
The article says, "Once we have an equation, we can use it to calculate something, but also for qualitative
and semi-quantitative reasoning." What does semi-quantitative mean? If something is at least quantitative
in part than we must consider it quantitative. What is the difference between semi-quantitative and simply
calculating something?
Statement: "We have to be careful not to write something that makes mathematical sense but is physical
nonsense."
Question: This statement refers to the topic that different kinds of quantities can't be added or equated.
Does this pertain to questions in Math class that find the relation between distance and time with a
moving object? Such as, "If a train is traveling x miles/hr when will it arrive at this destination?" because I
found this Physics question If two trains move towards each other at certain velocities, and a fly flies
between them at a certain constant speed, how much distance will the fly cover before they crash?" How
would time not be involved with this? You couldn't possibly calculate how long it would take for the trains
to crash towards each other while also calculating the speed which is probably miles per hour?
For the purposes of this class, will equations essentially be used to explore and define relationships
between certain variables instead of the common "plug and chug" method found in many math classes?
With the standard units being chosen arbitrarily, to what extent does the choice of unit affect the
necessary precision of the measurement being taken?
What are some of the most effective ways to determine which specific equation to use for a scientific
calculation in a situation where multiple equations are similar, or calculate similar things?
You say that math in science is not about numbers but if that is so then why do we speak in quantities
and values rather than conceptually on a more regular basis?
Do all fields of science have the same symbols for constants, or are they different for each field of
science?
How will we know what each symbol stands for in the case of "mathematical homonyms," especially if
they are in the same equation?
How do we know when two values can be equated or added
Are there values that we can consider proportional, even if they can not be equated using traditional
mathematical methods
If a problem involves the same symbol(T), can you assign a different symbol to differentiate between the
two (time and tension)?
Can mathematical equations and calculations also be used to measure and analyze qualitative data
within physics and biology?
When looking at mathematical homonyms, is using dimensional analysis a good way to determine the
difference between the same symbol in different contexts? Or should we just be able to tell from the
equation and other context clues for the most part?
How do we use equations to model a physical system?
The article mentions that math in science is about representing physical quantities; scientists use
mathematics to quantitatively deconstruct the world's they are exploring. However, there have been
instances in the past when certain mathematical models have produced bafflingly unexpected or
inexplicable results and in turn it seemed as if the math was giving rise to physical objects! Such was the
case in the evolution of physics from the end of the nineteenth century to the beginning/middle of the
twentieth century. Certain physical objects existed only within the realm of the theoretical until they were
discovered many years after their conceptualization. Still, this is not the case for every theorized object.
What precautions should scientists use in drawing conclusions from math applied to their understanding
of a physical concept? When can the greater community of biological scientists be sure that unique and
never-before seen mathematical results are actually describing some as-of-yet unearthed secret about
biology versus just being a case of runaway mathematical abstraction?
When you are representing a system with an equation how do you determine which variables are relevant
to include in the equation? When do you know to treat a variable as a constant or as a variable?
Why is it necessary for one symbol to have multiple meanings?
Why would an equation that is used to model a physical system be different from an equation that is used
in a math class to calculate something?...they are both equations and I am missing the big difference.
How often are mathematical models of systems accurate?
What is a parameter in physics? Can you give a more detailed example?
How can I know if something makes physical sense?
What is an example of an equation that mathematically makes sense, but doesn't make sense in a
physical context?
what is the most important thing you can tell another student on the issue "math in math is different from
math in science"?
In this class, at least in the beginning, will we be given guidance as to how to interpret a physical system
and create a model equation or will we be expected to know how to do this from the start?
As stated in the article an equation can be used to model a physical system. However, is there a set way
that we must have only one equation to model a physical system or could there by chance be two
equations with the same output that could both model the same physical system?
What are some practical ways, besides doing numerous practice problems, that we can truly grasp the
physical meaning of math?
The article mentions how there are conventional symbols used for certain quantities (ie m for mass). Will
we be given the conventional symbols to use for the quantities that we will be studying throughout the
course?
Even though for example, in "convention, physical scientists use m for a mass and t for a time" where do
we draw the line between creating our own variable (let's say I use 'x') and using conventional symbols? I
ask this due to this fact in the article in coexistence with this one: "In science, we have lots of different
kinds of symbols and they may shift from constant to variable depending on what we want to do". So,
even though we can assign a variety of variables, are there some variables/letters we can never assign to
certain quantities or measurements?
How much calculating will we do in this class?
If we are using a math to represent a physical situation, and we have two of the same quantities that
mean two separate things, how do we reflect that difference in a mathematical equation?
Is it at all possible to have a physics equation that uses only one symbol? If so, what would be its
significance, due to the fact that the vast majority of physics equations have many symbols used in many
different ways?
If using math in science, and specifically biology, is extremely important, why hasn't more biology related
math been introduced in my previous lower level biology classes? BSCI105 and 106 have little to no math
involved. Shouldn't there be consistency in all of the UMD courses leading to this one?
This article focuses on how math in science is different from math in math but I'm curious to know, how is
math in science similar to math in math?
How exactly can you tell qualitative information from an equation and a solution other than the measured
number?
Under reason 6, it says "Once we have an equation, we can use it to calculate something, but also for
qualitative and semi-quantitative reasoning." I see how to calculate an actual value, and to make
qualitative reasonings for an equation (e.g., 5 + x = 10; x = 5, and PV = nRT; P = (nRT/V) so decreasing
volume increases pressure, given all other variables remain constant), but what is semi-quantitative
reasoning?
in this article, they came up with some of the reasons that math is different when it comes to apply it in
sciences and real world than to just what it is in normal classroom types. but why they don't make them
similar to one another? why they don't familiarize us more with real world problems in math classes?
Also Why these differences came from the first place between these two worlds of math? how in sciences
using math is to represent information and their relationship towards one another but in other case would
just be finding the unknown?
Given that math in science has more rules and variables, does that mean that math in science is a better
approach (because of the need to understand conceptually) and should be used more often, or does it
over complicate something that could be easier simplified like math in math?
Because the physical world can have so many contributing factors and complexities, to what extent can
mathematical models accurately represent the world, and to what extent are these calculations and
models limited
If we define the symbol, can we use whatever symbols we would prefer or are there some universal
symbols we must use?
Why are the symbols from science are so different from math? Can't we just create new ones?
What do you mean by qualitative and semi-quantitative reasoning? I understand how an equation can be
used to calculate something, but how can you use an equation for reasoning?
How can using math help a scientist interpret the data for a physical system?
How can one be sure whether the calculations in science are accurate if they are not always defined as
clearly as those in math
What's the best strategy to figure out which mathematical equation to use in science/physical context?
Why does math in physics include many symbols, yet some symbols can stand for more than one
subject? Wouldn't it make more sense to have some more symbols in order to avoid confusion? Also, it
says that math is different when compared between pure and scientific, but in the end, isn't the final
process of an equation to obtain a formula that makes sense and plug in the numbers for variables to find
an answer, with the only difference being that you need to take into consideration the extra calculations to
convert between units??
Will we use any "pure math" in this course (I like math :D)?
How do mathematical equations help model a physical system to be better understood?
How does having dimensions and units differ from ordinary numbers?
In point number 5 it mentions that in pure math symbols are either variables or constants and in science
symbols can change roles depending on the purpose of the problem. which in fact is true. However, this
difference is ambiguous to me because couldn't symbols also change roles in pure math ?
Why does the meaning of a symbol need to change when used in different contexts? Wouldn't it be easier
to assign each symbol its own meaning or would this create too many symbols and meanings for
everyone to remember?
What is the best way to learn to recognize the "mathematical homonyms" or symbols that mean different
things in each context?