Notes, abstracts, papers, exams and problems of Mathematics

4.1 The stages of learning as Dienes
The learning process is a process based on abstraction, generalization and communication. This process of abstraction is to accurately analyze and Dienes identifies six different stages in it:
Stage 1: introduces the individual in the middle => Game Free
2nd stage: review, manipulate, get rules => Structured Games
3rd stage: becoming aware of the common structure to games made
4th stage: representation of the common structure graphically or schematically => Stage representative
5th stage study of the properties of abstract structure, which implies the need to invent a language => Stage symbolic
6th stage: Construction of axioms and theorems => formal Stage
Her pedagogical approach

System Types
The systems of equations can be classified by the number of solutions that can arise. According to that case may have the following cases:
· Incompatible system if it has no solution.
· Compatible system if you have any solution in this case can also distinguish between:
or compatible system determined when it has a finite number of solutions.
indeterminate or compatible system when it admits an infinite set of solutions.
Fitting and classification:

Calculating the rank of a matrix for determining

1. We can rule a line if:.
· All the coefficients are zeros.
· There are two equal lines.
• A line is proportional to another.
• A line is a linear combination of others.
Delete the third column because it is a linear... Continue reading "Matrices: multiplication, rank, determinant, inverse and Rouche-Frobenius theorem" »

Consider an European call option with strike equal to 10, T = 1, r = 0.05 and σ = 0.2. Using the following time-series:

1. For every time moment t = 0, 1/360, 2/360:

• Calculate the Black-Scholes price.
• Calculate the corresponding delta.
• Calculate the price of the corresponding replicating portfolio and its composition, if we consider a dynamic hedging.

2. Calculate a static hedging. What is the final value of the portfolio? Compare with the dynamic hedging results.

Solution

• At time 0, time to maturity is 1, and then
  • The Black-Scholes price is given by S0N(d1)−Ke−rT N(d2) = 10N(0.35)−10e−0.05N(0.15) = 1.0450
  • The Delta is given by N(d1) = N(0.35) = 0.6368
  • At time t = 0, the value of the replicating portfolio coincides with the Black-Scholes price

many people buy brands and give up wearing something that is an imitation fot not being true, and think that they will not give a good image to the rest.

On the one hand, it is true that they are of better quality and last longer,although imitations are sometimes very good too. A brand is also known all over the world. When they are seen by people, people want more of that original product. Your friends will not judge you if you wear something brand and will see you as someone who has money, when it shouldn't be this way. However, imitations are cheaper an seem original,you save money and the image you give is the same, since sometimes it noticed that it isn't imiation.

For me, imitations help people who want something and the original price... Continue reading "Good morning, have you got" »

Management of Interest Rate Risk

Major Risks in Bond Market

A) Interest Rate Risk (change in market prices of bonds due to varying interest rates)

• Increase in rates, decrease in market prices, increase in reinvestment rate risk (coupons reinvested at lower return)

B) Reinvestment Rate Risk (uncertainty of rate at which interim cash flows can be reinvested)

• High coupon rate, high reinvestment rate risk
• Greater for longer holding periods (high interim cash flows)

C) Default Risk (credit risk) (issuer unable/unwilling to pay interest and principal of bond)

• High credit rating, lower yield
• Short-term T-bills (almost risk-free, no default risk, and low return and reinvestment risk because of short duration)

D) Call Risk (risk bond issuer will redeem bond before... Continue reading "Interest Rate Risk Management: A Comprehensive Guide for Investors" »

Expense: Will it cost a lot of money for the municipality? Is it worth it?

Formal letter

We are writing in reference to your new products advised in March 23 edition of “Info Globe”. We are a software company based in Berlin which specializes in Games Development.

Our company is currently developing a new software to improve old games quality. We are interested in designing a new video game console which would works with old games with a better graphics quality.

 We would like to request a catalogue of your lasted collection that was advised in Info Globs. Please let us know if you would be interested in scheduling a meeting.

 I look forward to hearing from you.

Yours sincerely, M Walton

Faculty and Student Responses

A university president proposed that all students must take a course in ethics as a requirement for graduation. The table below gives the responses of a sample of faculty and students at the university when asked their opinion on this issue.

Y: FAVOR O: Oppose N: Neutral

Totals

F: Faculty         45             15             10                    70

S: Student        90             110             30                  ₂₃₀ 

 Totals   135               125                40

Probabilities

1. Find the following probabilities; each time ONE person is being randomly selected.

P(S or Y) = (230 + 135 – 90)/... Continue reading "Calculating Probabilities from a Table: Ethics Course Requirement" »