Building mathematicalcraving

How to Teach
Computer Science
while building
Mathematical craving

Welcome to All Participants
Prof NB Venkateswarlu
Professor, GVPCEW
Visakhapatnam
venkat_ritch@yahoo.com
www.ritchcenter.com/nbv

Let Me first
Congratulate all
the Organizers.

What am I going to talk?
• Status of Mathematical teaching in
Engineering- In my opinion
• Retrospection of possible reasons for the
prevailing pathetic situation.
• My perception about teaching
mathematics to Engineering Students
• My views about how to correct in a
humble manner

Remember I am only going to
share my experiences and
observations.
I am neither a Mathematician nor
a Computer Scientist. I try to be
an Engineer first though I know I
am still half-baked Engineer.

I got enlightenment about
Computer Science after reading
the book
Computational Geometry,
Preparata, Springer Series.

Also, I want to remind you I am
not going to be a fool by
promising that I can talk about
whole mathematics useful for
Engineers.
Only an Iota of it I shall
expose.

Join me to pay tributes to Sri
Ramanujam
8

As this Conference is organized in fond
memory of Sri Ramanujam, I love to
bring a recent post of my friend.

It reminds me number 1729.
11
Hardy said that it was just a boring
number: 1729.Ramanujan replied
that 1729 was not a boring number at all: it
was a very interesting one. He explained
that it was the smallest number that could
be expressed by the sum of two cubes in
two different ways.
There are two ways to say that 1729 is the
sum of two cubes. 1x1x1=1;
12x12x12=1728. So 1+1728=1729 But
also: 9x9x9=729; 10x10x10=1000. So
729+1000=1729 There are other numbers
that can be shown to be the sum of two
cubes in more than one way, but 1729 is
the smallest of them.

What are ground realities in our
education system?
13

You May love to see these
videos.
28
https://www.facebook.com/search/top/?q=m1%20badithulu

FB Groups
• B.Tech baditulu
• M1 baditulu

https://www.slideshare.net/venkatritch/appreciationof-mathematicsm

According to ACM 2001 Committee
A computer Science student should
posses a certain level of mathematical
sophistication such as:
• Ability to formalize concepts
• Work from definition
• Think rigorously
• Reason correctly
• And construct a theory

What does it take to become an
engineer?
• Mathematics
• Science
• Creativity

Whom we have to blame for this
worst situation?
• Parents
• Students
• Industry
• Universities or other controlling authorities
• College managements
• Lastly, faculty

I have illustrated problems related
to parents, managements,
Universities in my lecture hosted at:
http://www.slideshare.net/venkatritch/pedagogy-in-engineering-colle

Mathematics is hard!
Yes it is! But it is also very rewarding,
and is no more harder than learning to
skate or tennis! It takes time to
understand new ideas and concepts.
In any endeavour you need to do
something hard to excel!
BlockagesBlockages

You need to be bright to do
Mathematics.
No! You need not be very bright. But
Mathematics makes your brighter. And
it will improve your skills and
understanding of other related
subjects.
BlockagesBlockages

I don’t need a lot of Mathematics for
science!
Wrong! A higher level of Mathematical
skill will make you a better Scientist
and Engineer.
Great discoveries and higher level
performance in physics and
engineering innovation requires high
level Mathematics.
BlockagesBlockages

Rewards of doing Mathematics
• Problem solving skills that will help you in
every aspect of your life.
• Good organisational skills.
• Logical, clearer thinking.
• A very interesting, satisfying life full of
challenges and achievements!

By the way who are our current
Students in Engineering
colleges?

Of course, Who are our PhD
students and faculty vice versa?
Computers are great tools, however, without
fundamental understanding of engineering problems,
they will be useless.

Who are Our Students?:My
observations
• They put face that they did not hear
compound interest at all.
• If you probe further and throw hits and use
patting words, now some of their faces
glows.
• If you insist further, the answer is “sorry
we don’t remember the equation”.
• Some may write for final amount, but not
to interest.
P*(1+r/100)^t-P

Who are Our Students-Cont
• Simple interest =P*T*R/100
• If I say R is in ratio instead of percentage,
then also they don’t understand how to
change the equation.
• Of course, majority of them have 150 out
of 150 in Mathematics in their 10+2.

Do ask them about our
Intermediate Example on
Simple Pendulum
• Why do we draw the line?.
• To forecast g value at our place

An example: Grade to points
(They don’t have analysis skills.
They wait for answer for a
problem)
Grade Points
A (65) 10
B (66) 8
C (67) 6
D (68) 4
E (69) 2

They find very difficult to relate
to mathematics.
Answer: P=2*(70-g)
(65,10)
(69,2)
g
P

One More example from an US
based high school competition.
• Given a capital letter we need to find another upper case letter that
is d units from the given letter. You need to count cyclically.
• The following table is for a d value of 4
Input capital letter
with its ASCII code
Output capital letter
with its ASCII code
A(65) E(69)
E(69) I(73)
F(70) J(74)
V(86) Z(90)
W(87) A(65)
X(88) B(66)
Y(89) C(67)
X(90) D(68)

Not even 1% can think of
converting degrees in radians to
degrees, minutes and seconds.
Of course, I am skeptical about
the vice versa also.
• They don’t even remember how many
seconds makes a minute
• They don’t perceive that angle can be
more than 360 degrees.

Did you ever ask how they can
convert a given temperature in
one scale to all other scales.
• At most 40% can recall the equations.
• Only 10% recollects 273.03 correctly.

They take more time to related
to The World examples.
• Speed, Distance and Time
• Small examples involved bits, bytes, bps,
etc., is too confusing for them.
• May be a mathematics teacher has to
change from distance, time, speed to bits,
time and Mbps in the beginning itself

They find hard to relate to
mathematics.
How many digits are there in a
given integer?
What is the largest integer
which is integer power to 10 and
divides a given integer?

Guess from the following data?
Recall the definition of
logarithm.

log10(10)=1
log10(99)=1.99999999
log10(100)=2
log10(999)=2.99999999
log10(1000)=3
log10(9999)=3.99999999
log10(10000)=4
log10(99999)=4.99999999
log10(100000)=5
log10(999999)=5.99999999

They feel hard to understand
number of bits versus
logarithms?.

How to correct the situation?
• There can be hundreds of ways to correct.
Out of all, teaching mathematics should
be carried out with real life examples.
Preferably introduce feel of Engineering
along with the example. Of course, for this
to happen, mathematical faculty has to
enrich themselves with engineering
applications. Of course an Engg. Faculty
has to work in other way wrong. I
understand some UK university has
started a course “Mathematical
Engineering”.

My view is that mathematical
concepts should be explained with
possible live Engineering examples
at every possible level.
• Geometry
• Calculus
• Algebra
• Trigonometry

A practical example to illustrate
use of logarithms, simultaneous
equations. We want them to
appreciate mathematics and
develop interest in it. May be, I
am of the opinion is that to give
live examples as many as
possible to elucidate a concept.

Fitting Line – Least Squares
Approach

Linear Classifiers
fx yest
denotes +1
denotes -1
f(x,w,b) = sign(w x + b)
How would you
classify unknown
data?
w
x
+
b=0
w x + b<0
w x + b>0

Computer Graphics – Drawing a
Line

Area under a curve.
• Where is it practically used?
• In Civil Engg to calculate volume of cutting
and filling.

Confidence intervals – also
based on areas only
70

Air Pillows In Car to save
humans
• Head Injury Index (HIC) – Crash test and
air bags

Severity Index
• The first model developed historically was the Severity Index (SI).
• It was calculated using the formula:
• The index 2.5 was chosen for the head and other indices were used
for other parts of the body (usually based on possibly gruesome
experiments on human or animal bodies).
• The Severity Index was found to be inadequate, so researchers
developed the Head Injury Criterion ».

Head – Simple Pendulum
Motion

Braking
• Normal braking in a street car: 10 ms-2
(or about 1 g).
• Normal braking in a racing car: 50 ms-2
(or about 5 g).
This is due to aerodynamic styling and large tyres with
special rubber.
• When we stop in a car, the deceleration can be either
abrupt (as in a crash), as follows:
• or more gentle, as in normal braking:
• Either way, the area under the curve is the same, since
the velocity we must lose is the same.

Crash Tests
• Imagine a car travelling at 48.3 km/h (30
mph). Under normal braking, it will take
1.5 to 2 seconds for the car to come to
rest.
• But in a crash, the car stops in about 150
ms and the life threatening deceleration
peak lasts about 10 ms.

A3-ms value
• The A-3 ms value in the following graphs
refers to the maximum deceleration that
lasts for 3 ms. (Any shorter duration has
little effect on the brain.)

• If an airbag is present, it will expand and
reduce the deceleration forces. Notice that
the peak forces (in g) are much lower for
the airbag case.

• The blue rectangles in these deceleration
graphs indicate the most critical part of the
deceleration, when the maximum force is
exerted for a long duration.
• With an airbag, you are far more likely to
survive the crash. The airbag deploys in
25 ms.

Golden Ratio: Phi
Parthenon Greece

Leonardo da Vinci's "Vitruvian Man",
showing the golden ratio in body dimensions

Golden Ratio: Beauty’s Secret

Silver Ratio
Pell numbers: 1, 2, 5, 12,29
Silver ratio=1+sqrt(2)

Triangulation
90
In principle, epicenter the one point through which circles drawn from all the three seismic observatory
stations with the given distances as radius will pass through. This can be found by finding the intersection
points of two of the circles and then which of these two intersection points lies on the third circle.

Triangulation
• c= light speed
• ts=receiver clock offset time

An Image Processing
Example: IP and CG are
complimentary

Original, directional, Laplacian,
Sharpening

What are actually Eigen Values
and eigen vectors?.

An excellent example to
illustrate the use of orthogonal
vectors.
CDMA: Code Division Multiple
Access which is used in cell
phones, satellite phones, and
vice versa.

CDMA
• One channel carries all transmissions at
the same time
• Each channel is separated by code

CDMA: Chip Sequences
• Each station is assigned a unique chip sequence
• Chip sequences are orthogonal vectors
– Inner product of any pair must be zero
• With N stations, sequences must have the
following properties:
– They are of length N
– Their self inner product is always N

An excellent example to
illustrate the use of orthogonal
vectors.
CDMA: Bit Representation

Sequence Generation
• Common method: Walsh Table
– Number of sequences is always a power of two

How to teach rotation,
translation, etc with live
examples?

Operations of Photographs?
• Scaling
• Zooming
• Rotation
• Translation
All the above can be nicely introduced by
taking a simple image and using MATLAB
or paint or GIMP. Why a mathematics
teachers tries to be too abstract?

Example use in Robotics:
Kinematics and Dynamics.
Kinematics: Direct Kimematics: If we
apply a series of rotations and
translations where will be the robot
gripper? Inverse Kinematics: Also, what
rotations have to be applied at each
joint to position at a position. Dynamics
deals with stability of Robot.

Astronomy involves full of
rotations and transformations.

Estimating 3D information Two
Snaps – Binocular Vision.
It does involves number of
transformations.

Standard Deviation?. What for?
• Example of Production Process (Quality
Control Engineers)
• 0 ?. . There will be a taster, we takes a
piece of the prepared item and only if it
tastes good he will be sending for serving.
• Analyzing students marks of an
examination Center
• A companies share

What is the practical use of
Correlation?
• Hardly very few faculty really relates.
• How many of us ask the students to take x
and y co-ordinates of points on a line and
find correlation coefficient. Is this is same
as slope of a line? Do we relate? Rather,
both are different?
• Also, how many of us ask the students to
take x and y co-ordinates of points on a
circle and find correlation coefficient?. Do
we show them geometrically why they are

Correlation?( cont )
• Why we can not take data compression
example. Show what is DPCM, ADPCM,
etc by taking sound recording utility.
• You can simply explain about run-length
encoding.
• Introduce the word “auto-correlation” and
its implications in signal processing.

Correlation?(Cont)
• Radar Example to illustrate the use of
auto-correlation?
• Ask them about RADAR principle. Remind
them about echo principle.

Finite differences: relation
estimation from the observed
data on independent and
dependent variables.
10 15 20 25 30 35 40 50
101 210 389 643 878 1189 1634 2467

Do induce examples
• Ground water pollution
• Air pollution
• Oil reservoir modeling
• Digital Terrain modeling
• How a battery heats and fails

Newton Raphson Method
• Sqrt() function of C language
• Mathematics professor will not inform the
student that its is practically used in
mathematics library of C, C++, Java etc.
• While CSE faculty do not feel that he has
to refer Newton Raphson method while
introducing sqrt() function while teaching C
language. How a student can establish
relation? Leave about developing interest
in mathematics.

Gradient Descent Procedures
• Introduce local and global minima’s both in
one dimension, two dimensions, etc

What is a Determinant?.
An example from statistics. In
multivariate statistics,
covariance matrix represent
spread of points in the multi-
dimensional space. If
determinant is small then
samples are compact, otherwise
spread widely.

Recall “Stallin” Cinema
• If a fellow helps 3 people, and those three helps
3 each, and further they help three more, how
many
1+3 + 3*3 + 3*3*3 + 3*3*3*3 + …… 3^r =
= ½ * 3^(r+1) -1
If r=16 the sum is 6,45,70,031

Deadlocks in Networks
• Same as accidents on Roads

Search Engineer – To Divert the
Internet Traffic to Our Site

Click Based Charging –
AdWords of Google and Yahoo

A physics problem illustrated
mathematically. Why we can not do
in the same way in our class?

132
Newton’s 2nd
law of Motion
• “The time rate change of momentum of a body is
equal to the resulting force acting on it.”
• Formulated as F = m.a
F = net force acting on the body
m = mass of the object (kg)
a = its acceleration (m/s2
)
• Some complex models may require more sophisticated
mathematical techniques than simple algebra
– Example, modeling of a falling parachutist:
FU = Force due to air resistance = -cv (c = drag
coefficient)
FD = Force due to gravity = mg
UD FFF +=

m
cvmg
dt
dv
cvF
mgF
FFF
m
F
dt
dv
U
D
UD
−
=
−=
=
+=
=
v
m
c
g
dt
dv
−=
• This is a first order ordinary differential equation.
We would like to solve for v (velocity).
• It can not be solved using algebraic manipulation
• Analytical Solution:
If the parachutist is initially at rest (v=0 at t=0),
using calculus dv/dt can be solved to give the result:
( )tmc
e
c
gm
tv )/(
1)( −
−=
Independent variable
Dependent variable
ParametersForcing function

134
Analytical Solution
( )tmc
e
c
gm
tv )/(
1)( −
−=
t (sec.) V (m/s)
0 0
2 16.40
4 27.77
8 41.10
10 44.87
12 47.49
∞ 53.39
If v(t) could not be solved analytically, then
we need to use a numerical method to solve it
g = 9.8 m/s2
c =12.5 kg/s
m = 68.1 kg

135
)(
)()(
lim........
)()(
1
1
0
1
1
i
ii
ii
t
ii
ii
tv
m
c
g
tt
tvtv
t
v
dt
dv
tt
tvtv
t
v
dt
dv
−=
−
−
∆
∆
=
−
−
=
∆
∆
≅
+
+
→∆
+
+
))](([)()( 11 iii
tttv
m
c
gtvtv ii −−+= ++
This equation can be rearranged to yield
∆t = 2 sec
To minimize the error, use a smaller step size, ∆t
No problem, if you use a computer!
Numerical Solution
t (sec.) V (m/s)
0 0
2 19.60
4 32.00
8 44.82
10 47.97
12 49.96
∞ 53.39

t (sec.) V (m/s)
0 0
2 19.60
4 32.00
8 44.82
10 47.97
12 49.96
∞ 53.39
t (sec.) V (m/s)
0 0
2 16.40
4 27.77
8 41.10
10 44.87
12 47.49
∞ 53.39
m=68.1 kg c=12.5 kg/s
g=9.8 m/s
( )tmc
e
c
gm
tv )/(
1)( −
−= ttv
m
c
gtvtv iii
∆−+=+ )]([)()( 1
∆t = 2 sec
Analytical
t (sec.) V (m/s)
0 0
2 17.06
4 28.67
8 41.95
10 45.60
12 48.09
∞ 53.39
∆t = 0.5 sec
t (sec.) V (m/s)
0 0
2 16.41
4 27.83
8 41.13
10 44.90
12 47.51
∞ 53.39
∆t = 0.01 sec
CONCLUSION: If you want to minimize
the error, use a smaller step size, ∆t
Numerical solutionvs.

My views about how to correct
in a humble manner
• Let Professors of IIT’s or IISC’s or ISI or
Chennai Institute of Mathematics or TIFR
to form faculty interest groups and groom
them with necessary inputs to teach
mathematics more effectively in colleges. I
remember an example situation related to
Nanotechnology. I read some where that
what first Taiwan Government did is to
develop 5 to 10 examples to be taught at
school level to introduce Nanotechnology.
They did not grant research funds first!.

My views about how to correct in a
humble manner
• Build awareness among Mathematics
people about Engineering examples.
• Encourage combined lesson
development with excellent Engineering
examples by both mathematics and
engineering faculty.
• Develop teaching tools/models/prototypes.
• Encourage students to appear for
Mathematics Olympiad, Informatics
Olympiad.

My views on correcting the situation
• Is it possible to reduce class strength to
20-25?
• Is it possible to send faculty to class only
after orienting them to dogma of teaching?
• Is it possible to send only qualified faculty
to a course. In 4th
year level, “electives” are
taught by just passed faculty. Where as in
IIT’s, unless a senior professor of that
specialization retires, the next senior will
not get chance to teach that elective. What

My Views - Continued
• Project Expos by Mathematics and
Engineering departments.
• Seeing Engineering question papers to
have at least 30-40% of questions
involving mathematics.
May be give awards
to teachers
May be introduce awards
to students who answers more
mathematical answers more in
semester /year/whole 4 years
program.

My Views - Continued
• Maintaining a repository of live examples
and maintaining the same like the
following.

http://blog.pizzahut.com/flavor-news/national-pi-day-math-contest-p

https://pagez.com/2490/12-most-controversial-math-facts-that

Useful websites
• http://integralmaths.org
• http://www.teachengineering.org
• http://www.tryengineering.org
• http://www.intmath.com
• http://pumas.jpl.nasa.gov
• http://pumas.gsfc.nasa.gov
• http://www.citrl.net
• http://www.mathsisfun.com

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