2014-2015 Fall
To revise notes last semester, please go to https://docs.google.com/document/d/1r5Ic-zaT1_kS8HcTnVEcHeWRWcC5HSiW8lta4G50vsw/edit?usp=sharing. Please be reminded that there may be some typos and errors.
2014-2015 Spring
To revise notes last semester, please roll down to 2014-2015 Spring. Please be reminded that there may be some typos and errors.
2014-2015 Summer
Math 2411 - Applied Statistics
Announcements:
- Office: Rm 2612A
- Office Hours (MSC Area): Tuesdays 1400-1600
Fridays 1600-1800
- Midterm: Importance: 40% of total score
Date: July 22nd, 2015
Time: 1900-2100
Coverage: Chapters 1, 2 and 4.1
Result: [below average] [many students did not read the question]
Paper checking: [refer to Dr. Wong's email]
- Final Exam: Importance: 60% of total score
Date: August 13th, 2015
Time: 1800-2000
Coverage: All
Result:
Paper checking:
- Notes for this semester:
Tutorial 1 (June 22nd) : R [ppt]
Tutorial 2 (June 24th) : Basic counting and probability [notes] [answer]
Tutorial 3 (June 29th) : Conditional probability [notes] [answer]
Tutorial 4 (July 6th) : Discrete random variables [notes] [answer] [example 3]
Tutorial 5 (July 8th) : Continuous random variables [notes] [answer]
[Typo for Example 5: as mentioned in class, the solution should be X~N(10,9), not Bin(10,9)]
Tutorial 6 (July 13th) : Approximations [notes] [answer]
Tutorial 7 (July 15nd) : Data Analysis & Point Estimations [notes] [answer - amended on July 17th, 1800]
Tutorial 8 (July 20 & 22) : Confidence interval [notes] [answer - available since 1700 on 20th, as you may wish to have it before midterm]
Tutorial 9 (July 22nd) : Midterm Review [notes - amended on July 23th, 2200]
Tutorial 10 (July 27th) : Hypothesis testing [notes] [answer]
[Typo for Example 4(a): the alternative hypothesis H_1 should be ≠, instead of >
Still, we only need to consider f_{0.05}(9, 9) to see if H_1 is rejected or not.]
Tutorial 11 (July 29th) : Linear regression [notes] [answer]
Tutorial 12 (August 3rd) : Goodness of fit test [notes] [answer]
Tutorial 13 (August 5th) : ANOVA model [notes] [answer - amended on August 7th, 1100]
Revision for whole course (Final Exam) : [MATH2411_final_exam_formula_sheet.pdf (Pages 1 and 2 re-scanned) (Pages 1 and 2 again XD)]
In the midterm, many of you did not read the question; so please understand the question before you do anything this time.
Question 2 was supposed to be the easiest one, and your poor results in this question reflected that some of you might need
improvement in understanding the questions, which you may start with the most basic topic - counting - with its chapter [1][2][3][4][5][6][7]
2014-2015 Spring
Announcements:
- Notes for this semester (click the course): MATH 1013 (Calculus I), MATH 1014 (Calculus II), MATH 2741 (Geometric Constructions)
- Midterm: MATH 1013: March 26th, 1830-2030
MATH 1014: March 29th, 1015-1145
MATH 2741: April 10th, 1830-2000
- Results of Midterm: MATH 1013: Many of you still need to work hard, particularly those scored under 30 in midterm.
Mean is very low & variation is quite large, i.e. absolute grading is very likely to be applied.
If you keep this performance for the final exam, the failing rate will break its highest record.
MATH 1014: Please wait for the official results as this is a large-scale course in this semester.
Sorry that I got no "secret results" to tell.
MATH 2741: Out of 4 constructions (part a of first 4 questions), quite a number of you got 0 which is too poor.
A total of 18 pieces of your work (with "well done" screenshots) cannot be recorded by the
system, so you have to do the screenshots next time as well, in order to get your marks.
P.S. It happens that some students of came and asked question at 6pm on the day of midterm (which starts at 6.30pm), after I spent almost an extra hour at 4pm to teach another student about the course content. But I was rushing the last HW comments for the whole class (open-source exam) so I decided not to come out and answer anything. So please don't come at the last minute!! Your final exam timetable has already been announced, plan your studies earlier ^^
For all the 3 midterms that I invigilated, there are students going to the wrong place. So please do go to the correct examination venue!!
- Paper-cheking of Midterm: MATH 1013 April 10th, 1100-1200 Rm2612A
MATH 1014 (L1) April 16th, 1700 Rm 3472
MATH 2741 TBA
- Final: MATH 1013: May 26th (Tue.) 0830-1130 Venue: G017
MATH 1014: May 20th (Wed.) 1630-1930 Venue: Hall (for L1,2,3,4,6,8 only)
MATH 2741: May 22nd (Fri.) 0830-1430 Venue: Rm 3209A (TBC)
Everything for MATH 1014 is well-updated, plese plan your studies earlier.
The Maths Support Center would have normal opening hours until May 15th.
And extra opening hours on May 18th and 19th are as follows (Kitty's hour are on May 19th):
1100-1900 at Rm 2612B (the usual place) and 1900-2200 at Quiet Room, 1/F, UG Hall 2.
Math 1013 - Calculus I
To revise notes last semester, please go to https://docs.google.com/document/d/1r5Ic-zaT1_kS8HcTnVEcHeWRWcC5HSiW8lta4G50vsw/edit?usp=sharing. Please be reminded that there may be some typos and errors.
Week 1 (2015.02.02-06) [Notes] [Answer]
Exercises 1, 4-8, 10, 20, 34 would be done in class, as a demonstration; & the rest would be your practices.
Week 2 (2015.02.02-06) [Notes] [Answer]
Examples 1, 3, 9 and exercises 1, 2, 6 were done in class; & the rest would be your practices.
For exercise 6(d), the correct answer should be [0, 4] if you use the definition of decreasing in the book.
Week 3 (2015.02.16-18) [Notes] [Answer]
Exercises 1 to 4 and example 9 were done in class.
Students are strongly advise to do the rest before checking the answer.
Week 4 (2015.02.23-27) [Notes] [Answer]
Exercises 1 to 7 were done in class.
This is the last class of chapter 1 and students should make sure themselves be familiar with the properties of the trigonometric functions and their inverse, before moving to the next chapter.
Extra Exercise (February 2015) [Exercise]
For those who are not quite okay with elementary functions, especially the trigonometric functions, please make sure you can get at least 35 of them correctly on your own (without a calculator), in order to catch up with the upcoming contents.
Week 5 (2015.03.02-06) [Notes] [Answer]
- Hopefully we would go through exercises 1 to 10 in class.
- Sorry to tell that there is a typo in exercise 1 on page 4. For part (b), we are taking limit on sin(pi/x) instead of just pi/x.
- For both classes, we only ended on page 7 (exercise 3).
- Please go through the notes yourselves, and do the rest of the exercises.
- The progress in class was too slow. Please try to spend at most 3 minutes for each of the problems in the exercises.
Week 6 (2015.03.09-13) [Notes] [Answer]
- This would be our last class before doing dervative. You shall:
+ learn all the basic techniques in taking limit
+ be familiar with applying the limit laws and hence prove the (dis)continuity of a function
+ be able to sketch a function with its horizontal and vertical asymptotes
by the end of this week.
- Please be reminded that your midterm would be held 2 weeks later.
- For both classes, we went through all the examples and did exercises 1 and 2.
Please finish the rest and make that you are familiar with limits, because we are using it to define derivative later on.
Week 7 (2015.03.16-20) [Notes] [Answer] [Photos 1 and 2]
- Would definitely start differentiation.
- Please be reminded that if you are asked to find a function's derivative with its definition, then you cannot apply any rules.
- In class, we flipped through the examples and did exercises 1, 2, 3 and 23, the rest would be your own exercises.
- The proof of product rule was done in rush so I have attached photos of the proof here, for you as a reference.
Week 8 (2015.03.23-27) [Notes] [Answer]
- Past Midterm Paper was sent to students' HKUST email account. The FORMAT would be DIFFERENT.
- Derivatives of Trigonometric Functions, Implicit Differentiations, and Derivatives of Logarithmic Functions are included.
- On both classes, we went through all the examples.
- Please be reminded that you still have 2 days to go before midterm.
Week 9 (2015.03.29-04.02) [Notes] [Answer]
- Linearization, Newton's Method, and Maximum & Minimum Values would be included.
- For students who are taking the make-up midterm exam, please remember to bring your medical certificate to the venue.
- In yesterday's (March 30th) class, we did not have enough time to finish all the materials, so we will have part C in week 10.
Please try to do the exercises on absolute & local (aka relative) maximum & minimum, so as to speed up our classes in week 10.
Week 10 (2015.04.09-17) [Notes] [Answer]
- Mean Value Theorems and Derivatives & Graphs are included in this week's notes.
- Many of you didn't finish/try the problems we left last week, so we spent time for it during today's (April 14th) classes.
- Derivatives & Graphs is covered in today's class too, but Mean Value Theorem was left for next week as your paces were too slow.
- Please do the exercise yourselves as we do not have much time left, before the end of this semester.
Week 11 (2015.03.20-24) [Notes] [Answer]
- This week's notes includes l'Hopital's rule, curve sketching and optimization problems.
- In today's tutorials, we went through Mean Vaule Theorems, l'Hopital's Rule and curve sketching. Please do the exercises.
- Accordingly, we would have antiderivatives, areas & distances in week 12, definite (& indefinite) integrals, Fundermental Theorem of Calculus in week 13, and hence NO TIME LEFT for substitution rule. That means, we need an extra lesson. Please indicate to me your available time during [study break + final exam. period] for the extra tutorial if you wish to join. The google form would be available later. [For those who wish to have an extra tutorial class, please fill in the form ...(coming soon)...]
Week 12 (2015.04.27-30) [Notes] [Answer]
- Antiderivatives, Areas & Distances, and Definite Integrals are included in this week's notes.
- Hopefully we could finish all the topics by the Academic Week 13. Details about extra tutorial class would be announced when it is needed.
Week 13 (2015.05.04-08) [Notes] [Answer]
- The Fundamental Theorem of Calculus, Indefinite integrals & net change, and the substitution rule are included in this week.
- On the classes, I will mainly focus on the substitution rule and its exercises. For the definite & indefinite integrals, please do the exercises yourselves. If you do not have enough exercises, please feel free to come to the Maths Support Center to get some.
- As time is very tight, I would prefer you do the exercises and ask questions instead of any extra tutorial classes.
- The Maths Support Center would have normal opening hours until May 15th. And extra opening hours on May 18th and 19th are as follows: 1100-1900 at Rm 2612B (the usual place) and 1900-2200 at Quiet Room, 1/F, UG Hall 2.
Math 1014 - Calculus II
Class 1: Week 2 (2015.02.09-13) [Notes] [Answer]
§ Involves Fundermental Theorem of Calculus, distinguishing net change, and looking for areas between curves. Students are strongly advised to do the problems before the answers are available.
Class 2: Week 3 (2015.02.16-18) [Notes] [Answer] [Photos]
§ Covered slicing and cylindrical shell method. Problems are mainly about volumes.
§ Students in T1A (Thu. class) are strongly advised to go through the notes & ask immediately after the holiday if they have any questions.
Class 3: Week 4 (2015.02.23-27) [Notes] [Answer]
§ Work done, average value of a function, and arc length of curves are included.
§ Apart from summaries and examples, we would go through exercises 1a,b, 9 and 11a,b in class.
Class 4: Week 5 (2015.03.02-06) [Notes] [Answer]
§ Calculating surface area with the formula for arc length, and starting integration by parts.
§ Definition and properties of function, derivatives of trigonometric functions and their inverses, integration by substitution, etc. are the PRE-RESQUISITES of these topics / later weeks.
Warm reminder: You have already gone through a half before midterm, so please do revision ASAP, esp. for those who feel himself/herself has learnt nothing yet. XDD
Class 5: Week 6 (2015.03.09-13) [Notes] [Answer]
§ Continue with Integration by Parts, and start the new topic called Trigonometric Integrals.
§ In both class, we finished all the examples except 7, and went through exercises 1(a,b) and 13, and have a taste on either 14(a) or 15(a).
§ After talking with different parties, I agree that I was giving out too much solutions. Exercises are not examples, so I would gradually change my solutions to answer key.
Class 6: Week 7 (2015.03.16-20) [Notes] [Answer] [Photo]
§ On both classes, we went through all the examples, and did exercises 1.
§ Please be reminded that you only have about 10 days to go before midterm.
§ It is understandable that you may skip some classes during mid-term period. Students who missed the class may use the Photos of Whiteboard on 2015.03.16 as an aid for self-study.
Class 7: Week 8 (2015.03.23-27) [Notes] [Answer] [Photo]
§ In this week, we continued with polar coordinates and talked about approximate integrations. Please do the exercises before your midterm, especially the graph of polar coordinates that we didn't put much time on.
§ Please be reminded that the Math Support Center will be opened at 1100-1900 on Saturday 28th March, the day right before your midterm.
Class 8: Week 9 (2015.03.29-04.02) [Notes] [Answer]
§ Improper Integrals would be included.
Class 9: Week 10 (2015.04.09-17) Part 1 [Notes] [Answer]
§ Sequences and Series would be included.
§ Please vote for Part 2's content at the form
§ As mentioned in class, the solution for problem 16 is wrong. The correct one should be: "Since lim_{n->oo}\ {|a_n|} = oo, therefore, the sequence {a_n} is not bounded.
Class 10: Week 10 (2015.04.09-17) Part 2 [Notes] [Answer - refer to the notes of the corresponding week(s)]
§ As you voted, a revision on topics until week 8 (mainly weeks 1 to 7) would be covered in part 2 of week 10.
§ During classes, we mainly focused on the extended part of "Sequence and Series", and please do revision (of previous weeks) on your own.
§ We have to finish up all the tests (i.e. everything about series except Taylor and Maclaurin) by next week. Week 12 is reserved for Taylor and Maclaurin series while week 13 is for vectors and its products.
Class 11: Week 11 (2015.04.20-24) [Notes] [Answer]
§ Please revise yourself with all the tests we did in class (T1A on April 23rd & T1B on April 27th) & finish up the exercises.
§ Please feel free to go to the Math Support Center if you encounter any difficulties.
Class 12: Week 12 (2015.04.27-30) [Notes] [Answer]
§ Power series & Taylor and Maclaurin series would be included in this week.
§ On April 27th, we did a revision on all the tests (week 11's notes) and finished power series for this week.
§ Plannings for these days: -> on April 30th, finish the whole notes of week 12
-> on May 4th, get week 12's contents done + finish vectors & its addition & subtraction
-> on May 7th, finish everything about vectors
-> Extra tutorial (30 mins) during study break, go through dot and cross products of vectors
(Details to be announced in class on May 4th, Monday)
§ The answer for problem 10 is wrong, the correct one should be (-a,a).
Class 13: Week 13 (2015.05.04-08) [Notes] [Answer, for Problems 19 to 26 only]
§ In this week's notes and tutorial, only the three-dimensional coordinate systems, vectors, the addition and scalar multiplication are included. Please refer to the addtional notes for the dot & cross products of vectors, and go to the Math Support Center whenever you have any doubts about this subtopic.
§ Time is very tight so we decided not to arrange another extra tutorial on today's lesson. Instead, we ran the tutorial from 0930 to 1150 today (Monday's class). However, as most of you got another lesson after Thursday class so we surely cannot have it in the same way. Please do revise and ask questions at MSC.
§ The Maths Support Center would have normal opening hours until May 15th. And extra opening hours on May 18th and 19th are as follows: 1100-1900 at Rm 2612B (the usual place) and 1900-2200 at Quiet Room, 1/F, UG Hall 2.
Math 2741 - Geometric Constructions
Prior Office Hours for 2741 Students: Wed 1500-1600; Thu 1300-1400
You may wish to have a look on the comments of you homeworks.
[HW1] [HW2] [CW2] [HW3] [HW4] [HW6, CW6] [HW7] [CW7]
Those in red are the more general ones that many stduents would get, the underlined ones appear before in the red ones.
Moreover, you may wish to look at the solutions as well so they are here:
[HW1, HW2, CW2, HW3] [HW4, HW6, CW6, HW7] [CW6, CW7] [HW9, CW9, HW10, CW11, HW12, CW12 and Additional]
Week 1: First Crisis in Mathematics [ppt]
Week 2: Try your drawings on GeoGebra [Exercise]
(Students who are interested may also do it with real compass and straightedge)
Week 3: Remember how to write a proof? [Think about it]
- Students are strongly advised to proof the existances of the centers (including the centroid, circumcenter,
incenter, orthocenter) of a triangle.
- Students interested in geometry may try to proof the existance of the "nine-point circle".
Week 4: You would have field extension for this week. [-]
Week 5: Solving Cubic and Quartic Equations [ppt]
Taking cube root of 2 is a classical problem in compass-and-straightedge constructions.
With the aid of a marked ruler, we could solve cubic and quartic equations too.
How does it work? And what is a marked ruler?
Week 6: The content of this week would be your presentation. [-]
Week 7: Compass-only Constructions [Exercise as stated below]
Given 3 points A, B and C on a plane.
With compass only, find the four (or five) centers, namely centroid, circumcenter, incenter, & orthocenter
(& nine-point center), of △ABC.
Given 2 circles with radii r_1 and r_2.
Draw similar triangles with ratio of sides being r_1 / r_2.
With compass only, repeat everything you constructed with compass and straightedge given.
Week 8: Revision. [Repeat all the exercise you did, with and without the straightedge]
Week 9 (i.e. content of week 10): Midterm. [.]
Week 10: Straightedge-only Constructions [-]
With the starter set given, try out whether or not you are able to do what you have in the past,
e.g. addition, subtraction, multiplication and division of any 2 given lengths.
Can you still bisect a line segment or an angle like what you had before, any essential elements for doing so?
Week 11: Poncelet-Steiner Theorem & Regular Polygons [refer to Canvas modules]
The contents of Weeks 10 and 11 are combined so I am not intend to give out any extra notes / exercises to you.
For those who do wish to practice more, repeat what you constructed with compass and straightedge give.
What you've constructed in the past: Centers of a Triangle, and hence the Circumcircle and In circle of 3 points
Center of a Circle
Tangents of a Circle at a Given Point
Common tangents of Two Given Circles
& etc.
Week 12: Theory of Constructible Regular Polygons. [.]
Deadline of ALL homeworks for weeks 10 and 11.
Week 13: Finish those left from previous weeks [refer to Canvas modules]