### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# 672 Class Note for MATH M0050 at Purdue

### View Full Document

## 31

## 0

## Popular in Course

## Popular in Department

This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 31 views.

## Similar to Course at Purdue

## Reviews for 672 Class Note for MATH M0050 at Purdue

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15

Tips on Writing in Mathematics Notes An important purpose of courses like Math 244 Elementary Real Analysis and Math 252 Abstract Algebra is to learn to write proofs and other more or less formal mathematical paragraphs The style and language of mathematical writing may not seem especially natural at rst sight Butiwith practice and experienceione soon nds that adhering carefully to mathematical writing conventions actually simpli es and streamlines the process of writing proofs and it helps assure that your ideas are intelligible to others Here then are some useful tips for writing proofs and prooflike prose in mathematics 1 Write in complete sentences quot The quotes are there because mathematical sentences in mathematics may include not just ordinary words but also symbols equations inequalities etc For instance it s ne to write Because I gt 3 we know 12 gt 9 and 13 gt 27 On the other hand it s usually not good form to write zgt3z2gt913gt27 One problem with the latter is that there s no connective tissue The reader canlt tell whether you re listing your favorite inequalities asserting that something implies something else or what 2 Use punctuation capital letters and other standard grammatical niceties These devices are used in ordinary English to help the reader see clearly what s being said or implied Consider for instance the different possible meanings of this notice supposedly posted near an Australian beach crocodiles donlt swim here Would you swim here or not ls the sign intended for human or reptile readers In practice many mathematical sentences convey complex ideas and so naturally have correspond ingly complex structures lt7s especially important therefore to write mathematics in as clear and unambiguous a manner as possible and to give the reader every possible aid in deciphering meaning 3 Be sure your sentences scan Proofs and solutions must be not only correct but also intelligible to a reader An excellent way to assure the latter is to read each sentence back to yourself Doing this silently rather than aloud may reduce ridicule from neighbors A sentence with proper English grammar and syntax may be mathematically right or wrong Every mathematician has seen eloquently expressed proofs that boil down to nonsense But a sentence without these attributes is almost surely wrong or worse meaningless to a reader 4 Be clear Thatls easily said but admittedly not easily done complicated or difficult ideas are naturally hard to express clearly But the work is worth doing and practice is essential Giving you practice with and feedback on your mathematical writing is an important part of courses like ERA and Abstract Algebra 5 Use standard mathematical symbols and notations and use them in standard ways For instance the notations 13 13 and 13 all have precise but different meaningsione is an open interval one is a closed interval and one is a set with just two members Violating these conventions arbitrary as they may be is asking for trouble It is far from clear for instance what such notations as I 12 gt 2 and Q 7V2 really mean By contrast the expressions 112gt2 and IEQ12gt2 are clear and unambiguous 6 Take care with word order Because mathematical language conveys complex thoughts word order can be crucial Consider these two statements For every 6 gt 0 there exists an integer n such that 0 lt ln lt 6 There exists an integer n such that 0 lt ln lt e for every 6 gt 0 The rst statement is true its a version of what s sometimes called the Archimedean principle for real numbers The second statement is false 7 Just say no to it The harmlesslooking word it commits countless crimes in mathematics For example the connection between stationary points of f and roots of f has sometimes been put as vaguely as this It is maximum or minimum when its at and that happens when its a zero of its derivative Thatls just too many pronouns and it s far from clear what each one refers to Just say no A function f may have a maximum or minimum value where the graph of f is at This can occur at a value of I which is a root of the derivative function f 8 Make it look easy A musician planning a recital invests hours of practice and study and hits plenty of false notes The recital itself however skips all the practice and study and most of the false notes In the same way a nished mathematical proof should be the polished result rather than the basic process of whatever informal thinking experiments and false starts may have contributed along the way While it s sometimes okay to include some record of the investigative phase of proving a result it s important not to confuse such material with the proof itself The best proofs are clear concise and couched in standard mathematical language 9 Don t say too muchior too little Respect but donlt overtax your readers intelligence and willingness to work Ideas in your proof should be clear and accessible to your readerisomeone with your own level of intelligence and knowledge

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.