तत् सवितुर्वरेण्यं | भर् गो देवस्य धीमहि | धियो यो नः प्रचोदयात् || (ऋग्वेद ३.६२.१०)

We meditate upon the effulgent glory of the divine light; may it illumine and inspire our intellect.

**Prof. Ram's
(Ramsamujh) FIUnix01 Homepage**

**Office: DM 419E, Telephone:
305-348-2929, Fax:
305-348-6158,**

**e-mail:
ramsamuj@fiu.edu** Math
Dept page link
Abbreviated C.V.

**
-----------------------------------------------------------**

**FIU Fall 2021 Repopulation Aug 20th, 2021**

**FIU
Fall 2021 Repopulation Aug 13th, 2021**

**
FIU Panther Book
Pack Information**

Every student is automatically enrolled for the Panther Book Pack (https://onestop.fiu.edu/bookpack/) at the

time that you register for classes. The program will cover your textbooks for each course at a charge of $20

per credit hour.
We suggest that you compare this to the cost of all your required
course materials.

If this total is higher than the Panther Book Pack
Cost, **
you can opt out at any point from the
day you **

**
receive your Panther Book Pack email
until three days after the add/ drop date on the Academic **

**
Calendar for that term. **For
the Fall 2021 this day is September 2, 2021.

*
*

clicking on the Panther Book Pack tile and then clicking the opt-out / opt-in toggle for the session you

would like to change your participation status for. If you have any further questions, please check out

the link (https://onestop.fiu.edu/bookpack/) also given above .

**
-----------------------------------------------------------**

**Courses
for FALL 2021, On-Campus classes**

1.
Linear Algebra: MAS 3105.U03 (90600) -
GC 279B, Final Exam Scores and
Grades (Fall 2021)

*Regular Class Time is
11:00 am - 12:15 pm; Tue, Thu*.
FIU Classes begin on Aug. 23rd,
2021.

**Exam
#1** for Linear Algebra is on ** Thursday**,
**Oct. 07th**, 2021
during regular class time.

**Exam
#2** for Linear Algebra is on ** Tuesday**,
**Nov. 23rd**,
2021 during regular class time. **Final Exam**
for Linear Algebra is on ** Thursday**, **Dec.
09th**, 2021 from **09:45 ** AM** - 11:45**
AM

(**FINAL
EXAM TIME is
confirmed by FIU.**)

2.
Intro
to Combinatorics:** **MAD
4203.U01(82156) - RB 140, Final Exam Scores & Grades (Fall
2021)

*Regular Class Time is 2:00
pm - 3:15 pm; Tue, Thu*. FIU Classes begin on Aug. 23rd,
2021.

**Exam
#1** for Intro to Combinatorics is on **Thursday**,
**Oct. 07th**,
2021 during regular class time.

**Exam
#2** for Intro to Combinatorics is on
** Tuesday**, ** Nov. 23rd**,
2021 during regular class time. **Final Exam**
for Combinatorics is on **Thursday**,** Dec.
9th**, 2021 from **12:00 ** PM **- 02:00**
PM

(**FINAL
EXAM TIME is
confirmed by FIU.**)

**Prof. Ram's O****ffice
hours (via Zoom): **
* 12:45pm-1:45pm
& 3:45pm-4:45pm * Tue & Thu.

Prof. Ram's Office hours Zoom Meeting ID - 722 280 1561. A Passcode will be sent to your official FIU e-mail.

If you did not receive a passcode, please send an e-mail to ramsamuj@fiu.edu

No LA (Learning Assistant) or TA
(Teaching Assistant) for the above courses were available*. *

**
-----------------------------------------------------------**

**Courses for
SPRING 2022 -
EVERYTHING IS VERY TENTATIVE
**

Spring Break (No Classes) Monday-Saturday, February 28th, 2022 - March 5th, 2022.

1. Linear Algebra: MAS 3105.U01 (Course #11701) - Final Exam Scores & Grades (Spring 2022)

*Regular Class Time is 09:30
am - 10:45 pm;Tue, Thu.* FIU Classes begin on Mon. Jan.
10th,
2022.

**Exam #1**
for Linear Algebra is on ** Thursday**,
**Feb. 24th**, 2022
during regular class time.

**Exam #2**
for Linear Algebra is on **Thursday**,
** April** 7**th**,
2022 during
regular class time.

**Final
Exam** for Graph Theory is on
**Tuesday**,** Apr.
19th**, 2022 from
**09:30am** **- 11:45am**

(**FINAL
EXAM TIME is NOT YET
confirmed by FIU.**)

2. Differential Equations:
MAP 2302.U02 (Course
#12507)
-** **Final Exam Scores & Grades (Spring
2022)

*Regular Class Time is
11:00 am - 12:15 pm;
Tue, Thu.*
FIU Classes begin on Mon. Jan.10th,
2022.

**Exam
#1** for Differential Equations** **is on **Thursday**, Feb**
10**, 2022
during regular class time.

**Exam
#2** for Differential Equations** **is on **Thursday**, Mar**
??**, 2022
during regular class time.

**Exam
#3** for Differential Equations is on
**Thursday**, **April ??th**,
2022
during regular class time.

**Final
Exam** for Differential Equations is on
**Thursday**,** Apr.**
**21st**, 2022 from
**09:30am**
**- 11:45am**

(**FINAL EXAM TIME is NOT YET confirmed by FIU.**)

3. Theory of Algorithms: MAD 3512.U01 (Course #11711) - Final Exam Scores & Grades (Spring 2021)

*Regular Class Time is * * 02:00 pm - 3:15 pm;
Tue, Thu.*
FIU Classes begin on Mon.
Jan. 10th, 2022.

**Exam
#1** for Theory of Algorithms is on **Thursday**,
**Feb. 10th**, 2022
during regular class time.

**Exam
#2** for Theory of Algorithms is on
**Thursday**, ** April
7th**, 2022
during regular class time.

**Final
Exam** for Theory of Algor. is on
**Thursday**,** Apr.
21st**,
2022 from **12:00pm**
**- 02:00**pm.

(**FINAL EXAM TIME is NOT YET confirmed by FIU.**)

**Prof. Ram's O****ffice
hours**: 12:30pm - 1:15pm and 3:30pm - 4:30pm
Tue & Thu.

The Learning Assistant for the above courses
**is not known as yet.**

*(Tentative schedule.) *
**Times:**

**
-----------------------------------------------------------****Class
Notes for Several Classes**

Hand-written
class notes are available for some classes. Just click and check on the page
for "class notes."

1. Axiomatic
Set Theory 2. Graph
Theory 3. Intro
to Advanced Math 4. Intro
to Combinatorics

5.
Linear Algebra 6. Mathematical
Logic 7. Theory
of Algorithms 8.
Differential Equations

Puzzles&
Games** ** **
-** Fun stuff for when you might be bored.

**Tutoring Services: **

**FIU
Centre for Academic Success**, GL 120, MMC.

**DISCLAIMER**: The
data in this homepage is considered accurate but is not guaranteed. In
this age of computer hackers

there is also no guarantee that someone may not have tampered with the contents. So if there is anything that looks fishy,

or if there are last minute cancellations or changes to test dates, please check with Professor Ram first, before acting on

that information. Professor Ram is not known for making last minute changes - and will only do so if absolutely necessary.

If there is ever any need for any such change he will announce it in class.

**
-----------------------------------------------------------**

**General information for ALL courses taught at
FIU**

**
1.**
**Over-rides for getting into a full class :**

(a) We cannot give out over-rides **until the
first class meeting** because we have to **ensure that the
classroom has space for everyone**

to whom we give an over-ride. (The classroom is sometimes listed as TBA and changes are often made just before classes start.).

If you wish to
get into a full class, **please come to the first class meeting **and we will
try to accommodate everyone, if possible.

(Over-rides will be given out in the order of your GPA - the students with higher GPAs will get preference. So please bring an informal

copy of your transcript with
you. **If you have no transcript, no over-rides will be
given.**)

(b) For **multi-section courses** we cannot
give out any over-rides **unless all the sections are
full**. Over-rides can be given out only at

the first class meeting. In order for you to get an over-ride, I need proof that you satisfied the prerequisites for the course - only then will

I be able to give your **Name, Panther ID, and the Course
Details** to the Math Department designated Advisor (currently
Prof. John Zweibel)

who is the only one who is allowed to enter this information into the system. Once the advisor does this, you will be able to register.

Please keep in mind that the advisor may have hundreds of over-ride requests to process, so it might take up to 24 hours to get yours into the system.

(c) For courses such as MAD 3512 (which are run every semester) the number of over-rides we can give is restricted - and may be as small as zero.

The number of over-rides we give will depend, in part, on the enrollment in the the course course of the chronologically-next semester of the previous

year. This is because we want to ensure that the course runs each semester. In many cases, the Summer semesters (and sometimes Fall semesters)

get low enrollments. When the enrollment in any semester drops below 20, the course is automatically cancelled & this prevents many (as much as 19)

students from graduating. So sometimes we have to give no over-rides in order to make sure the course runs the next semester.

** 2**.
**Cancellation of Tests or Quizzes & Rest Room Breaks**:

If a TEST or Quiz is cancelled due to a HURRICANE or other emergency, the TEST or Quiz will be given on the first meeting of the class after the

hurricane or emergency. You should check the FIU website (if you have power) or call the FIU hotline (or the Miami-Dade Hurricane emergency hotline)

for the latest updates about hurricanes. If you need to go to the Rest Room while taking a test, you will always be allowed to do so, but after you come

back from the Rest Room, you must finish the rest of the test in a different colored ink, so that it will be clear what you did before going to the Rest Room

and what you did after coming back. If there is a significant difference between the two sets of solutions, your paper will be submitted to the relevant

University Academic body to determine whether or not you committed any misconduct.

**
3.** **Make-up Tests:**

If you missed the
**first test** in the semester for an allowable, legitimate, verifiable
reason you may be able to take a make-up exam as long as you provide

**adequate documentation** and **notify the professor at
within two hours of the scheduled exam time**. You must take the
make up test on the first

opportunity you get to return to school. The allowable reasons are restricted to medical emergencies, traffic accidents in which your car becomes

non-functional on your way to the exam, and deaths in the immediate family (parents, siblings, children). We are not allowed to give make-up tests

for work related issues. As always you must provide
documentation. If you miss a **quiz **or a** later exam**, you will
not get a make-up; your other

scores will instead be used (with their corresponding weights) to produce your final grade.

** 4.** **Incomplete
grades:**

In order to get an
**incomplete grade, IN, **the total points in the tests or quizzes you took
must add up to a total **at least 50% of the total course points**,

ou must
have an **overall passing grade in the tests and quizzes taken so far**, and
**the reason you missed the Final Exam must be an allowable, **

**legitimate,
verifiable one**. The allowable reasons are restricted to medical
emergencies, traffic accidents in which your car becomes non-functional on

your way to the exam, and deaths in the immediate family (parents, siblings, children). We are not allowed to give make-up Final Exams for work related issues.

You must also inform (via e-mail or phone) the professor
in charge,** within two hours of the scheduled Final Exam time**,
and provide all documentation

before you take the make-up Final Exam. Failure to provide the proper documentation by the end of the first week of the following semester will result

in a zero score in the Final Exam and the grade which that entails. You usually have until the end of the following semester to actually take the make-up

Final exam but you are encouraged to do so
as early as possible. Make-up Final Exams** cannot** be given in the
Semester break.

**5.** **Attendance
Policy**:

Class attendance is
**mandatory** but allowances will be made for illnesses, emergencies, and
officially sanctioned religious holidays (provided your professor

is notified about at least 2 weeks before such holidays) as long as the total amount of absences do not exceed 40%. If, for whatever reason, you attend

less
than 60% of the classes, you will automatically be assigned a failing grade and
you **may** have to pay back the university any subsidy that you received.

(Please check with Registration & Financial Aid about this.) If you anticipate that you will not be able to reach the 60% threshold (because of severe injury,

prolonged illness, or other problems), please inform the registrar as soon as possible and try to get a withdraw or a late drop. Your professor cannot

help you in these circumstances - only the registrars can - and the earlier you tell them about the problem, the better it will be for you.

**
-----------------------------------------------------------**

*Medeis ageometretos eisito mou ten
stegen. *[Let no one who is ignorant of Geometry/Mathematics
(unjust) proceed any further.]

We can easily forgive a child who is afraid of the dark; the real tragedy of life - is when men are afraid of the light. The beginning is the

most important part of the work. Love is
a serious mental disease. Ignorance - the root & the stem of every evil.
* Plato (427-347 BCE)*

*Amicus Plato - amicus Aristoteles - magis
amica veritas.* Plato is my friend - Aristotle is my friend - but my
greatest friend is truth.

If I have seen further it is only by standing on the shoulders of giants. To explain all nature is too difficult a task for any one man

or even for any one age. 'Tis much better to do a little with certainity, and leave the rest for others that come after you,

than to explain all things by conjecture
without making sure of any thing. *Isaac Newton
(1643-1727)*

Napole*'*on : *Ils m'ont dit
que vous avez e'crit ce grand livre sur le syste`me de l'univers, et que vous n'avez me^me jamais mentionne' son Cre'ateur.*

[They tell me you have written this large book on the system of the universe, and (that you) have never even once mentioned its Creator.]

Laplace
(1749-1827): *Je n'ai pas besoin de cette hypothe`se la`.*
* *[I had no need of that hypothesis.] - *apocryphal story by
Rouse Ball*

The difference between genius and
stupidity is (simply this): genius has its limits (stupidity has
none). *Alexandre Dumas-fils (1824-1895)*

Everything should be made as simple as possible but not any simpler. If we knew what we were doing, it would not be called research, (now) would it?

Science without (the fervor of) religion is
lame; religion without (the realization that) science (is the only way to
the truth) is blind.* A. Einstein (1879-1955)*

*Es gibt keinen Gott und Dirac ist sein
Prophet* - There is (definitely) no God and Dirac is His (the
true) messenger.

If you are receptive and humble, mathematics
will lead you by the hand (to the greatest truths).
*P.A.M. Dirac (1902-1984)*

अर्धाली १: बंदौं प्रथम
महिसुर्चरना |
मोहजनित
संसय
सब
हरना **
|| ** (रामचरितमानस,
बालकाण् ड १.३)

अर्धाली २: बिनु
सतसंग बिबेक न
होई | रामकृपा बिनु
सुलभ
न सोई
**|| **
(रामचरितमानस, बालकाण्
ड २.४)

Before I commence
the divine tale, I first bow to the feet of the masters of wisdom on
earth because they remove all doubts born out of
ignorance.

Wisdom dawns not without the association of the
enlightened and such communion is
only possible by the grace of the Universal One. *Tulsidas (1532-1623)*

काल
करे
सो
आज
कर
आज
करे
सो
अब
| पल
में
परलय
होएगी
बहुरि
करोगे
कब ** || **(कबीर दास)

Whatever you have to do tomorrow, do today; whatever you have to do today, do (right away) now.

For
when the moment has passed, the task at hand can never be done somehow*.** **Kabir** Das (1448?-1518?)*

Natural Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But this book cannot be understood

unless one first comprehends (masters) the language of mathematics - for without it, one is doomed to (forever) wander in the darkest labyrinth.

In all questions of science (truth), the authority of a thousand million (believers) is not worth the humble reasoning of a single (rational) individual.

The ancient scriptures teaches us (supposedly)
how to go to heaven - not how the heavens go! (paraphrased) * Galileo
Galilei (1564-1642*)

[Galileo Galilei believed the Earth revolved around the Sun. For this, he was interrogated by the Inquisition, was put on trial, found guilty and sentenced to

indefinite imprisonment. For renouncing his former beliefs before the Cardinals that judged him, he was allowed to serve this time instead under house-arrest.]

*------------------*

COURSES
THAT WERE TAUGHT AT FIU

Adv. Calculus (Analysis) I Axiomatic Set Theory Calculus I Calculus II

Calculus
III (Multivariable) Combinatorics
Differential
Equations Discrete
Mathematics

Graph
Theory
History
of
Math
Introd
to Adv. Math Introd
to
Analysis

Linear
Algebra
Mathematical
Logic Theory
of Algorithms UGrad. Indep. Study

Grad
Math
Logic Grad Real Analysis Grad
Set
Theory Grad. Indep. Study

** MISCELLANEOUS
STUFF**
Miscellaneous Puzzles&
Games
Math
Jokes** **

Math Jokes Math Limericks Video clips

OLD COURSE DATA

**COURSES FOR
FALL 2020 & SPRING 2021 at FIU**

Graph Theory: MAD 3305.U01 (Course #?) - Final Exam Scores & Grades (Spring 2021)

Theory of Algorithms: MAD 3512.U0? (Course #?) - Final Exam Scores & Grades (Spring 2021)

Intro to Adv. Math: MAA 3200.U01 (Course #?) - Final Exam Scores & Grades (Spring 2021)

Linear Algebra: MAS 3105.U02 (83110) -
Final Exam Scores and
Grades (Fall 2020)

Theory of Algorithms: MAD 3512.U01 (82429)) - Final Exam Scores & Grades (Fall 2020)

Intro to Combinatorics: MAD 4203.U01(82416) - Final Exam Scores & Grades (Fall 2020)

**COURSES FOR
FALL 2019 & SPRING 2020 at FIU**

Graph Theory: MAD 3305.U01 (11914) - Final Exam Scores & Grades (Spring 2020)

Theory of Algorithms: MAD 3512.U01 (11915) - Final Exam Scores & Grades (Spring 2020)

Intro to Combinatorics:MAD 4203.U01(82748) - Final Exam Scores & Grades (Fall 2019)

Theory of Algorithms: MAD 3512.U01 (82764) - Final Exam Scores & Grades (Fall 2019)

Intro
to Advanced Math: MAA
3200.U01 (82763) -** **Final
Exam Scores & Grades (Fall 2019)

**COURSES FOR FALL 2017
& SPRING 2018 at FIU**

Differential Equations: MAP 2302.U01 (32887) - Final Exam Scores & Grades (Spring 2018)

Graph Theory : MAD 3305.U01 (33134) - Final Exam Scores and Grades (Spring 2018)

Theory of Algorithms: MAD 3512.U01 (33137) - Final Exam Scores & Grades (Spring 2018

Graph Theory : MAD 3305.U01 (99616) - Final Exam Scores and Grades (Fall 2017)

Intro to Combinatorics:MAD 4203.U01(99644) - Final Exam Scores & Grades (Fall 2017)

**COURSES FOR FALL 2016
& SPRING 2017 at FIU**

Differential Equations: MAP 2302.U01 (32887) - Final Exam Scores & Grades (Spring 2017)

Graph Theory : MAD 3305.U01 (33134) - Final Exam Scores and Grades (Spring 2017)

Theory
of Algorithms: MAD 3512.U01 (33137) - Final
Exam Scores & Grades (Spring 2017*)*

Graph Theory : MAD 3305.U01 (82217) - Final Exam Scores and Grades (Fall 2016)

Combinatorics :MAD 4203.U01 (82303) - Final Exam Scores and Grades (Fall 2016)

**COURSES FOR FALL 2015
& SPRING 2016 at FIU**

Theory of Algorithms : MAD 3512.U01 (12553) - Final Exam Scores and Grades (Spring 2016)

Graph
Theory
**
****-
** MAD 3305.U01 (81983) - Final
Exam Scores and Grades (Fall 2015)

Intro
to Combinatorics ** ****-
**MAD 4203.U01 (82092) - Final
Exam Scores and Grades (Fall 2015)

Intro
to Advanced Math
**-** MAA 3200.U01 (82121)
-** **Final
Exam Scores and Grades (Fall 2015)

**COURSES FOR FALL 2014
& SPRING 2015 at FIU**

** **MAD 3305.U01 (16224)
- Final
Exam Scores and Grades (Spring
2015)

**
**
MAD 3512.U01 (16226) - Final
Exam Scores and Grades (Spring 2015)

Graph
Theory
**
****
**
MAD 3305.U01 (81724) - Final
Exam Scores and Grades (Fall 2014)

Intro
to Combinatorics ** ****
**MAD 4203.U01 (85082) - Final
Exam Scores and Grades (Fall 2014)

Intro
to Advanced Math
MAA 3200.U01 (90408)
-** **Final
Exam Scores and Grades (Fall 2014)

**COURSES
FOR FALL 2013 & SPRING 2014 at FIU**

Linear
Algebra
MAS 3105.U01 (10454) -
Final
Exam Scores and Grades (Spring 2014)

Theory
of Algorithms MAD 3512.U01(10448) - Final
Exam Scores and Grades (Spring 2014)

Differential
Equations MAP 2302.U03 (80572) - Final
Exam Scores and Grades (Fall 2013)

** **MAD 3512.U01
(80569) - Final
Exam Scores and Grades (Fall 2013)

**COURSES
FOR FALL 2012 & SPRING 2013 at FIU**

Differential
Equations**
**MAP 2302.U01 -
Final
Exam Scores and Grades (Spring 2013)

Graph Theory MAD 3305.U01 - Final Exam Scores and Grades (Spring 2013)

Linear
Algebra** **
MAS 3105.U02 - Final
Exam Scores and Grades (Spring 2013)

Theory of
Algorithms MAD
3512.U01 - Final Exam
Scores and Grades (Fall 2012)

Intro to Advanced Math MAA 3200.U01 - Final Exam Scores and Grades (Fall 2012)

**COURSES
FOR FALL 2011 & SPRING 2012 at FIU**

Calculus
I MAC 2311.U17 - Final
Exam Scores and Grades (Spring 2012)

Calculus
II
MAC
2312.U11 - Final Exam Scores and Grades (Spring 2012)

Theory
of
Algorithms MAD 3512.U01 - Final
Exam Scores and Grades (Fall 2011)

Multivariable
Calculus
MAC 2311.U03
- Final Exam Scores and Grades (Fall 2011)

Graduate Set Theory MHF 5107.U01 - Independent Study Course (Fall 2011).

**COURSES FOR FALL 2009
& SPRING 2010 at FIU**

Calculus
I ** **
MAC
2311.U11 - Final Exam Scores and Grades (Spring 2010)

Theory
of
Algorithms
MAD 3512.U01 -
Final Exam Scores and Grades (Spring 2010)

Theory of
Algorithms MAD 3512 -
Final Exam Scores and Grades (Fall 2009)

Calculus
II ** **
MAC
2312 - Final Exam Scores and Grades (Fall 2009)

**COURSES FOR FALL
2008 & SPRING 2009 at FIU:**

Theory
of
Algorithms MAD 3512 - Final
Exam Scores and Grades (Spring 2009)

Axiomatic
Set
Theory MHF 4102 - Final
Exam Scores and Grades (Spring 2009)

History
of Mathematics MHF
3404 - Final Exam Scores and Grades (Spring 2009)

Introd
to Advanced Math MAA
3200 - Final Exam Scores and Grades (Fall 2008)

Differential
Equations MAP
2302 - Final Exam Scores and Grades (Fall 2008)

**NOTE**: Many of the files for old
tests and solutions for courses that I am not currently teaching are temporarily
removed

because they take up a lot of my allocated webspace. So those links will lead nowhere. I keep the links so I can just

put back the files (and remove others) and then gain access when I teach those particular courses. Also some of the links

n the last group above lead nowhere because this homepage is still (and, probably, will always be) under construction.

Buena suerte y que dios
los bendiga.