Link to blog post: http://raffysaldana.blogspot.com/2009/11/photos-amc-125-class-of-dr-saldana-nov.htmlClick on the link below to see larger images:
http://www.facebook.com/album.php?aid=172097&id=682835049&l=5f9bacbd32
.
Showing posts with label AMC 125. Show all posts
Showing posts with label AMC 125. Show all posts
Wednesday, November 18, 2009
Photos: AMC 125 Class of Dr. Saldaña (Nov. 2009)
Link to blog post: http://raffysaldana.blogspot.com/2009/11/photos-amc-125-class-of-dr-saldana-nov.htmlClick on the link below to see larger images:
http://www.facebook.com/album.php?aid=172097&id=682835049&l=5f9bacbd32
.
Tuesday, November 10, 2009
AMC 125: Lecture No. 1. Introduction to Probability Theory
.
Link to blog post: http://raffysaldana.blogspot.com/2009/11/amc-125-lecture-no-1-introduction-to.html
AMC 125 – Mathematics for Computer Science II
Dr. Rafael P. Saldaña
Mathematics Department
School of Science and Engineering
Ateneo de Manila University
rsaldana@ateneo.edu
Lecture No. 1. A FIRST WORD ON PROBABILITY
Source: Grimaldi, 150 - 156.
TOPICS:
1. EXPERIEMENT
2. SAMPLE SPACE
3. DEFINITION OF PROBABILITY
Under the assumption of equal likelihood, let S be the sample space for an experiment E. Each subset A of S, including the empty subset, is called an event. Each element of S determines an outcome, so if S = n and a is an element of S, A is a subset of S, then
Pr({a}) = The probability that {a} (or, a) occurs = {a}/S, = 1/n, and
Pr(A) = The probability that A occurs = A/S = A/n
Note: We often write Pr(a) for Pr({a})
EXAMPLES:
1. When you toss a fair coin, what is the probability that you will get a head?
2. If you toss a fair die, what is the probability that you will get
(a) a 5?
(b) a 6?
(c) a 5 or a 6?
(d) an even number?
(e) an odd number?
3. There are 20 students enrolled in Dr. Saldana's class. If Dr. Saldana wants to select two of his students, at random, he may make a selection in (20 2) = 190 ways, so S = 190.
Suppose that Ace and Bob are two of Dr. Saldana's students in class.
Let A be the event that Ace is one of the students selected and B be the event that the selection includes Bob.
What is the probability that Dr. Saldana selects
a. Both Ace and Bob?
b. neither Ace nor Bob?
c. Ace but not Bob?
to be continued...
.....
Link to blog post: http://raffysaldana.blogspot.com/2009/11/amc-125-lecture-no-1-introduction-to.html
AMC 125 – Mathematics for Computer Science II
Dr. Rafael P. Saldaña
Mathematics Department
School of Science and Engineering
Ateneo de Manila University
rsaldana@ateneo.edu
Lecture No. 1. A FIRST WORD ON PROBABILITY
Source: Grimaldi, 150 - 156.
TOPICS:
1. EXPERIEMENT
2. SAMPLE SPACE
3. DEFINITION OF PROBABILITY
Under the assumption of equal likelihood, let S be the sample space for an experiment E. Each subset A of S, including the empty subset, is called an event. Each element of S determines an outcome, so if S = n and a is an element of S, A is a subset of S, then
Pr({a}) = The probability that {a} (or, a) occurs = {a}/S, = 1/n, and
Pr(A) = The probability that A occurs = A/S = A/n
Note: We often write Pr(a) for Pr({a})
EXAMPLES:
1. When you toss a fair coin, what is the probability that you will get a head?
2. If you toss a fair die, what is the probability that you will get
(a) a 5?
(b) a 6?
(c) a 5 or a 6?
(d) an even number?
(e) an odd number?
3. There are 20 students enrolled in Dr. Saldana's class. If Dr. Saldana wants to select two of his students, at random, he may make a selection in (20 2) = 190 ways, so S = 190.
Suppose that Ace and Bob are two of Dr. Saldana's students in class.
Let A be the event that Ace is one of the students selected and B be the event that the selection includes Bob.
What is the probability that Dr. Saldana selects
a. Both Ace and Bob?
b. neither Ace nor Bob?
c. Ace but not Bob?
to be continued...
.....
Course Syllabus: Mathematics for Computer Science II (AMC 125)
.
AMC 125 – Mathematics for Computer Science II
Dr. Rafael P. Saldaña
Mathematics Department
School of Science and Engineering
Ateneo de Manila University
rsaldana@ateneo.edu
1. Schedule
1030 – 1130, MWF, SEC A–303
2. Prerequisite
Passing grade of AMC 124
3. Textbook
Discrete and Combinatorial Mathematics: An Applied Introduction, 5th edition
by R. P. Grimaldi. Pearson Education, Inc., 2004.
4. Course Outline and Time Frame
4.1. PROBABILITY (9 hours)
4.2. RINGS (10 hours)
4.3 GROUPS (10 hours)
Long Test 3, Tentative: Friday, February 12, 100 pts
4.4 CODING THEORY (11 hours)
Long Test 4, Tentative: Friday, March 12 100 pts
Final Exam (Comprehensive): 200 pts
5. Course Requirements and Grading System
The final mark of the students will be based primarily on the following:
Final Grade = (Student’s Total Score/Total Possible Score) * 100%
Percentage of the total Score // Equivalent letter grade
92% - 100% : A
86% - 91% : B+
77% - 85% : B
69% - 76% : C+
60% - 68% : C
50% - 59% : D
49% and below F
6. Class Policies
6.1. Cellular phones shall be turned off during class hours.
6.2. Maximum number of absences is 9 hours.
6.3. The teacher may send anyone out of the classroom due to discourtesy
to the teacher or to a fellow student, misbehavior in
the classroom, and other reasons found in the Student Handbook.
6.4. A student who misses an exam may be given a make-up exam
depending on the student’s reason(s), and upon the Department
Chairperson’s approval. Make-up exams are more difficult
than the regular exam.
6.5. Any form of cheating is not allowed. Refer to the Student Handbook
for details.
6.6. Use bond paper in all tests. Do not use pencil in all tests. No
borrowing and/or lending of calculators.
6.7. A student with a prefinal class standing of 90% maybe exempted
from taking the final exam.
7. Additional Important Dates to Remember
Date // Day // Event
11/13/09 Friday, 2nd Sem Faculty Day
11/30/09 Monday, Bonifacio Day
12/08/09 Tuesday Feast of the Immaculate Conception
12/20/09 – 01/03/2010 Christmas Break
02/01/10 Monday ADMU President’s Day
02/22/10 Monday People Power Day
8. Consultation Hours
MWF 1530-1700
Dr. Rafael P. Saldaña
Mathematics Department
School of Science and Engineering
Ateneo de Manila University
rsaldana@ateneo.edu
1. Schedule
1030 – 1130, MWF, SEC A–303
2. Prerequisite
Passing grade of AMC 124
3. Textbook
Discrete and Combinatorial Mathematics: An Applied Introduction, 5th edition
by R. P. Grimaldi. Pearson Education, Inc., 2004.
4. Course Outline and Time Frame
4.1. PROBABILITY (9 hours)
- The Axioms of Probability
- Conditional Probability
- Discrete Random Variables
4.2. RINGS (10 hours)
- The Ring Structure
- Ring Properties and Substructures
- Ring Homomorphisms and Isomorphisms
4.3 GROUPS (10 hours)
- Definition and Elementary Properties of Groups
- Homomorphisms, Isomorphisms, and Cyclic Groups
- Cosets and Lagrange’s Theorem
Long Test 3, Tentative: Friday, February 12, 100 pts
4.4 CODING THEORY (11 hours)
- Elements of Coding Theory
- The Hamming Metric
- The Parity-Check and Generator Matrices
- Group Codes: Decoding with Coset Leaders
- Hamming Matrices
Long Test 4, Tentative: Friday, March 12 100 pts
Final Exam (Comprehensive): 200 pts
5. Course Requirements and Grading System
The final mark of the students will be based primarily on the following:
- 4 Long Tests; cancel the lowest score (300 points)
- Final Exam (200 points)
- Optional: Quizzes, Assignments (100 points max)
Final Grade = (Student’s Total Score/Total Possible Score) * 100%
Percentage of the total Score // Equivalent letter grade
92% - 100% : A
86% - 91% : B+
77% - 85% : B
69% - 76% : C+
60% - 68% : C
50% - 59% : D
49% and below F
6. Class Policies
6.1. Cellular phones shall be turned off during class hours.
6.2. Maximum number of absences is 9 hours.
6.3. The teacher may send anyone out of the classroom due to discourtesy
to the teacher or to a fellow student, misbehavior in
the classroom, and other reasons found in the Student Handbook.
6.4. A student who misses an exam may be given a make-up exam
depending on the student’s reason(s), and upon the Department
Chairperson’s approval. Make-up exams are more difficult
than the regular exam.
6.5. Any form of cheating is not allowed. Refer to the Student Handbook
for details.
6.6. Use bond paper in all tests. Do not use pencil in all tests. No
borrowing and/or lending of calculators.
6.7. A student with a prefinal class standing of 90% maybe exempted
from taking the final exam.
7. Additional Important Dates to Remember
Date // Day // Event
11/13/09 Friday, 2nd Sem Faculty Day
11/30/09 Monday, Bonifacio Day
12/08/09 Tuesday Feast of the Immaculate Conception
12/20/09 – 01/03/2010 Christmas Break
02/01/10 Monday ADMU President’s Day
02/22/10 Monday People Power Day
8. Consultation Hours
MWF 1530-1700
Wednesday, November 19, 2008
AMC 125: Lesson, November 19, 2008
.
Topic: Ring Properties
pp. 677 - 679, Grimaldi
Definition 3: Multiplicative Inverse
Let R be a ring with unity u.
If a ∈R and there exists b∈R such that ab=ba=u,
then b is called a multiplicative inverse of a and a is called a unit of R.
(The element b is also a unit of R.)
Definition 4: Let R be a commutative ring with unity. Then
a) R is called an integral domain if R has no proper divisors of zero
b) R is called a field if every nonzero element of R is a unit.
Group Activity:
Study Example 14.6 on page 678
Graded Activity (To be submitted)
Answer completely problem no. 9 on pages 678 - 679.
.
Topic: Ring Properties
pp. 677 - 679, Grimaldi
Definition 3: Multiplicative Inverse
Let R be a ring with unity u.
If a ∈R and there exists b∈R such that ab=ba=u,
then b is called a multiplicative inverse of a and a is called a unit of R.
(The element b is also a unit of R.)
Definition 4: Let R be a commutative ring with unity. Then
a) R is called an integral domain if R has no proper divisors of zero
b) R is called a field if every nonzero element of R is a unit.
Group Activity:
Study Example 14.6 on page 678
Graded Activity (To be submitted)
Answer completely problem no. 9 on pages 678 - 679.
.
Monday, November 17, 2008
AMC 125: Rings and Modular Arithmetic
.
TOPIC: RINGS AND MODULAR ARITHMETIC
(Grimaldi, 673 - 679)
Definition 1.0 Ring Structure
Let R be a nonempty set on which we have two closed binary operations, denoted by + and ⋅ (which may be quite different from the ordinary addition and multiplication to which we are accustomed). Then (R, +, ⋅) is a ring if for all a,b,c ∈R,the following conditions are satisfied:
a) a + b = b + a (Commutative Law of + )
b) a + (b + c) = (a +b) + c (Associative Law of +)
c) There exists z ∈R such that a+z = z+a=a foe every a∈R.(Existence of an identity for +)
d) For each a ∈R there is an element b∈R with a + b = b + a = z (Existence of inverse under +)
e) a ⋅(b⋅c)=(a⋅b)⋅c (Associative Law of ⋅)
f) a⋅(b+c)=a⋅b+a⋅c (b + c) ⋅a=b⋅a+c⋅a ( Distributive Laws of . over +)
Note: + refers to ring addition and ⋅ refers to ring multiplication
Definition 2.0 Ring with Unity
Let (R, +, ⋅) be a ring.
a) If ab=ba for all a,b ∈R, then R is called a commutative ring.
b) The ring R is said to have no proper divisors of zero if for all a∈R, b∈R,ab=z⇒a=z or b=z.
c) If an element u∈R is such that u≠z and au=ua=a for all a∈R,we call u a unity, or multiplicative identifty , of R. Here R is called a ring with unity.
Graded Activity: Study Example 14.3, page 675 (Grimaldi). Answer the following question (to be submitted): Define the binary operations ⊕ and ⊙ on Z by x⊕y=x+y-7 and x⊙y=x+y-3xy, for all x,y∈Z. Question: Explain (completely) why (Z,⊕,⊙) is not a ring.
.
TOPIC: RINGS AND MODULAR ARITHMETIC
(Grimaldi, 673 - 679)
Definition 1.0 Ring Structure
Let R be a nonempty set on which we have two closed binary operations, denoted by + and ⋅ (which may be quite different from the ordinary addition and multiplication to which we are accustomed). Then (R, +, ⋅) is a ring if for all a,b,c ∈R,the following conditions are satisfied:
a) a + b = b + a (Commutative Law of + )
b) a + (b + c) = (a +b) + c (Associative Law of +)
c) There exists z ∈R such that a+z = z+a=a foe every a∈R.(Existence of an identity for +)
d) For each a ∈R there is an element b∈R with a + b = b + a = z (Existence of inverse under +)
e) a ⋅(b⋅c)=(a⋅b)⋅c (Associative Law of ⋅)
f) a⋅(b+c)=a⋅b+a⋅c (b + c) ⋅a=b⋅a+c⋅a ( Distributive Laws of . over +)
Note: + refers to ring addition and ⋅ refers to ring multiplication
Definition 2.0 Ring with Unity
Let (R, +, ⋅) be a ring.
a) If ab=ba for all a,b ∈R, then R is called a commutative ring.
b) The ring R is said to have no proper divisors of zero if for all a∈R, b∈R,ab=z⇒a=z or b=z.
c) If an element u∈R is such that u≠z and au=ua=a for all a∈R,we call u a unity, or multiplicative identifty , of R. Here R is called a ring with unity.
Graded Activity: Study Example 14.3, page 675 (Grimaldi). Answer the following question (to be submitted): Define the binary operations ⊕ and ⊙ on Z by x⊕y=x+y-7 and x⊙y=x+y-3xy, for all x,y∈Z. Question: Explain (completely) why (Z,⊕,⊙) is not a ring.
.
Monday, November 10, 2008
ACM ICPC Philippines 2008: Cebu Institute of Technology Participants
.
Name of School/Institution: Cebu Institute of Technology
Address: N. Bacalso Avenue, Cebu City
Contact Person: Larmie S. Feliscuzo
Position in School/Institution: Chair, IT Dept.
Full Name of Coach:
1. Larmie S. Feliscuzo
Full Name of Contestants / Age / Year Level and Course
(Including Alternates)
1. Lawrence Ranario / 18 / 3-BS Computer Science
2. Eugene Busico / 19 / 4-BS Information Technology
3. Jufni Rizada / 19 / 4-BS Information Technology
4. Rahima Hamis / 18 / 3-BS Computer Science
.
Name of School/Institution: Cebu Institute of Technology
Address: N. Bacalso Avenue, Cebu City
Contact Person: Larmie S. Feliscuzo
Position in School/Institution: Chair, IT Dept.
Full Name of Coach:
1. Larmie S. Feliscuzo
Full Name of Contestants / Age / Year Level and Course
(Including Alternates)
1. Lawrence Ranario / 18 / 3-BS Computer Science
2. Eugene Busico / 19 / 4-BS Information Technology
3. Jufni Rizada / 19 / 4-BS Information Technology
4. Rahima Hamis / 18 / 3-BS Computer Science
.
Class List, AMC 125 B, Math for Computer Science II, SY 2008-2009
.
AMC 125 B - MATH FOR COMPUTER SCIENCE II
School Year 2008 , Semester 2
SALDANA, RAFAEL P.
Class Number / Name
1. ALABASTRO, REGINE PAULINE GONZALES
2. ANATALIO, ALYSSA NICOLE MASANGKAY
3. ANDRES, JUAN MIGUEL LIMJAP
4. ANG, JANLEBRAD BILANES
5. CASUGBU, ANNA RAISA CRISELDA PECHARDO
6. CHEN, LANCELOT ERIC ANG
7. CHENG, JOSHUA REX TAN
8. CHOA, JAMES ANDREW CHUNG
9. DOROMAL, LORENZO MIGUEL SORIANO
10. DYKIMCHING, ALYSSA MARIE TE
11. FERNANDEZ, MARIKA GIANINA HIZON
12. GO, DANIEL KRISTOFFER REYES
13. GO, JANSSEN MARWIN LAM
14. GULOY, NICOLE GUBALLA
15. KOH, CHRISTIAAN KESSLER GOMEZ
16. LEE, JAN AARON ANGELO TE
17. LEE, KEN DARIONE ANG
18. LEYSON, JAN CHRISTIAN MARCELO
19. LIGUNAS, MARIA CLARISSE TERUEL
20. LIM, CHESTER CHIU
21. MADERAL, CHRISTEENA ANDREA LATORRE
22. MANAYSAY, ABEL MARCK ABUNGAN
23. PASCUAL, KRISTINE ESTER DE LEON
24. ROTH, JUERGEN KENNETH NAVARRO
25. SEARES, MELISSA CAMELLA BERJAMIN
26. SY, JOHN ERIC SO
27. TAÑEDO, VICTOR PATRICK GUEVARA
28. TIU, HOLVIN G
29. TOBIAS, TOBI CAPARAS
30. UMALI, KEVIN BJORN VILLANUEVA
31. VALERIO, DYLAN KEMUEL MAYNIGO
32. YBAÑEZ, MICHAEL FERRER
.
AMC 125 B - MATH FOR COMPUTER SCIENCE II
School Year 2008 , Semester 2
SALDANA, RAFAEL P.
Class Number / Name
1. ALABASTRO, REGINE PAULINE GONZALES
2. ANATALIO, ALYSSA NICOLE MASANGKAY
3. ANDRES, JUAN MIGUEL LIMJAP
4. ANG, JANLEBRAD BILANES
5. CASUGBU, ANNA RAISA CRISELDA PECHARDO
6. CHEN, LANCELOT ERIC ANG
7. CHENG, JOSHUA REX TAN
8. CHOA, JAMES ANDREW CHUNG
9. DOROMAL, LORENZO MIGUEL SORIANO
10. DYKIMCHING, ALYSSA MARIE TE
11. FERNANDEZ, MARIKA GIANINA HIZON
12. GO, DANIEL KRISTOFFER REYES
13. GO, JANSSEN MARWIN LAM
14. GULOY, NICOLE GUBALLA
15. KOH, CHRISTIAAN KESSLER GOMEZ
16. LEE, JAN AARON ANGELO TE
17. LEE, KEN DARIONE ANG
18. LEYSON, JAN CHRISTIAN MARCELO
19. LIGUNAS, MARIA CLARISSE TERUEL
20. LIM, CHESTER CHIU
21. MADERAL, CHRISTEENA ANDREA LATORRE
22. MANAYSAY, ABEL MARCK ABUNGAN
23. PASCUAL, KRISTINE ESTER DE LEON
24. ROTH, JUERGEN KENNETH NAVARRO
25. SEARES, MELISSA CAMELLA BERJAMIN
26. SY, JOHN ERIC SO
27. TAÑEDO, VICTOR PATRICK GUEVARA
28. TIU, HOLVIN G
29. TOBIAS, TOBI CAPARAS
30. UMALI, KEVIN BJORN VILLANUEVA
31. VALERIO, DYLAN KEMUEL MAYNIGO
32. YBAÑEZ, MICHAEL FERRER
.
Subscribe to:
Posts (Atom)
Posts
