# Types Of Insects, Types Of

## Types Of Insects

Contents

- 1 Types Of Insects
- 2 A Detailed Guide on the Many Different Types of Crude Oil
- 3 Hop Variety Descriptions
- 4 26 Different Types of Mathematics
- 5 26 Types of Math
- 5.1 1. Algebra
- 5.2 2. Geometry
- 5.3 3. Trigonometry
- 5.4 4. Calculus
- 5.5 5. Linear Algebra
- 5.6 6. Combinatorics
- 5.7 7. Differential Equations
- 5.8 8. Real Analysis
- 5.9 9. Complex Analysis
- 5.10 10. Abstract Algebra
- 5.11 11. Topology
- 5.12 12. Number Theory
- 5.13 13. Logic
- 5.14 14. Probability
- 5.15 15. Statistics
- 5.16 16. Game Theory
- 5.17 17. Functional Analysis
- 5.18 18. Algebraic Geometry
- 5.19 19. Differential Geometry
- 5.20 20. Dynamical Systems (Chaos Theory)
- 5.21 21. Numerical Analysis
- 5.22 22. Set Theory
- 5.23 23. Category Theory
- 5.24 24. Model Theory
- 5.25 25. Mathematical Physics
- 5.26 26. Discrete Mathematics

What are types of insects? Insects are invertebrates. Insect’s body is made of three parts: the head, the thorax and the abdomen. The head has two antennas, eye and mouth device which takes the place of mouth. The thorax insects is always have a three pairs of legs. Most types of insects developed important changes during their lives. These changes of form and activities the insects undergo during their development are called metamorphosis.

Insect size varies greatly varying in length from 0.2 mm (Mymaridae, Hymenoptera) and 350 mm (Micadina phictenoides, Phasmida). Most types of insects are harmful to human and animals. Certainly, larvae and adults devour potato plants, leaves and tree trunks, fruit trees and much more. In addition, some species of mosquitoes, bugs, flies are large carriers of diseases and infections. On the contrary, other types of insects are very useful to man. For example, ladybugs feed with insect pests. Without good bugs who eat`s the bad, harmful; many crops would be destroyed. Insects play an important role in plant life. For example they provide pollination of a large number of cultivated plants useful to man.

When an insect sits on a flower, she takes with her grains of pollen which is fixed on the body and legs. When flying on another flower of the same species, she leaves a part of pollen there, and so takes place the fecundation. That’s why insects such as bee are useful. In the first place, the bee produce wax and honey. Silkworms are used to manufacture the silk; they were discovered by more than 4000 years in China. Finally, several people feed with some types of insects. Some types of insects may be perceive ultraviolet light, invisible to people.

What for us is a butterfly of a dull white, for butterfly male is different. In the world of insects, sounds and smells are used often to find a partner. Almost every species play different roles. Some of them are quiet strange,like moths, for example,who ensures salt and humidity, absolutely necessary for their life, sucking buffalo tears. Other types of insects, endowed with a strong anti-freeze, who populate snowy peaks of the mountains and spend their lives digging after bugs that have died of cold. Speaking about ants ,them don`t have a ruler is a particularly remarkable .Taking into account that some colonies of ants can count more than 20 million members! And yet, this “metropolis” of insects is working perfectly, each ant has her own role established, so that entire colony is providing food, protection and shelter.

Perhaps the most impressive example of shelter for insects is the termite’s mound. Some of these mounds have a height of 7.5 meters. These architectural wonders are equipped with sophisticated air conditioning and with underground gardens of mushrooms. But most amazing is that the termites that build these castles are blind!

About 30% of our food depends on the pollination performed by bees, most of which are wild. Insects keep earth clean through an efficient system of recycling the dead plants and animals. In this way, soil is fertilized, and nutritional substances resulting from here help plant growth.

www.typesof.com

## A Detailed Guide on the Many Different Types of Crude Oil

Some people arbitrarily speak about oil as if it is a single, indistinguishably homogenous substance without any unique differentiation, but this is actually not the case at all! In fact, there are many different kinds of oil.

In its natural, unrefined state, crude oil ranges in density and consistency, from very thin, light weight and volatile fluidity to an extremely thick, semi-solid heavy weight oil.

There is also a tremendous gradation in the color that the oil extracted from the ground exhibits, ranging all the way from a light, golden yellow to the very deepest, darkest black imaginable.

For the purpose of having a set, agreed upon “vocabulary,” the petroleum industry often uses references to “Geographical Locations” in order to descriptively classify crude oils.

This is due to the fact that oil from different geographical locations will naturally have its own very unique properties. These oils vary dramatically from one another when it comes to their viscosity, volatility and toxicity.

The term “viscosity” relates to the oil’s resistance to flow. Higher viscosity crude oil is much more difficult to pump from the ground, transport and refine.

The term “volatility” describes how quickly the oil evaporates into the air. Oils that are naturally highly volatile need additional effort to ensure that temperature regulation and sealing procedures loose as little oil as possible.

The term “toxicity” refers to how dangerously poisonous the oil & its refining processes are to local life, from humans, to flora and fauna as well as other environmentally fragile living entities and organisms. If an oil spill were to occur, each type of oil presents quite unique “clean up” challenges, procedures and priorities!

The four primary types of oil are:

(1) **The Very Light Oils / Light Distillates** which include: Jet Fuel, Gasoline, Kerosene, Light Virgin Naphtha, Heavy Virgin Naphtha, Petroleum Ether, Petroleum Spirit, and Petroleum Naphtha. These oils tend to be highly volatile and can evaporate within just a couple of days, which quickly diffuses and decreases toxicity levels.

(2) **Light Oils / Middle Distillates** which include: Most Grade 1 and Grade 2 Fuel Oils and Diesel Fuel Oils as well as Most Domestic Fuels and Light Crude Marine Gas Oils.

These oils are moderately volatile, less evaporative and moderately toxic.

(3) **Medium Oils** : Most of the crude oil on the market these days falls into this particular category. Low volatility makes for messier & more complex “clean ups” and when it comes to the increased toxicity levels, I believe we have all lived long enough to see what “Medium Oil” spills can do to the local ocean life out on the seas or local wildlife right here on “terra firma!”

(4) **Heavy Fuel Oils** which include the heavy crude oils, Grade 3,4,5 and 6 Fuel Oils (Bunker B & C) as well as Intermediate and Heavy Marine Fuels. With these oils there is very slow and little evaporation and therefore toxicity is highly increased. This not only means potentially severe contamination for fish, fowl and fur-bearing creatures, but possible “long term” contamination of water and soil as well.

In fact, there are actually over 160 different oils traded on the market theses days, but for simplicity’s sake, let’s discuss the three primary oils that get most of the serious attention in the news and in the markets.

**West Texas Intermediate** (WTI) is an extremely high quality crude oil which is greatly valued for the fact that it is of such premium quality, more and better gasoline can be refined from a single barrel than from most other types of oil available on the market.

The WTI “API Gravity” is 39.6 degrees, which makes it a “light” crude oil, with only 0.24 percent sulfur, which makes it a “sweet” crude oil. The term “API Gravity” refers to

the “American Petroleum Institute Gravity, which is a measure that compares how light or heavy a crude oil is in relation to water. If an oils “API Gravity” is greater than 10 then it is lighter than water and will float on it. If an oils “API Gravity” is less than 10, it is heavier than water and will sinks.

These combined qualities as well as location make WTI a prime crude oil to be refined in the United States, which is by far, the largest gasoline consuming country on the planet. The vast majority of WTI crude oils are refined in the Midwest and Gulf Coast regions. Even with production of WTI crude oil in decline, WTI is often priced from $5 to $7 higher per barrel than “OPEC Basket” oil and on average, $1 to $2 higher per barrel than “Brent Blend” oils.

**Brent Blend** is actually a combination of different oils from 15 fields throughout the Scottish Brent and Ninian systems located in the North Sea. Its “API Gravity” is 38.3 degrees, which makes it a “light” crude oil, but clearly not quite as “light” as WTI. It also contains about 0.37 percent sulfur, which makes it a “sweet” crude oil, but then again, not quite as “sweet” than WTI.

Brent Blend is quite excellent for making gasoline and middle distillates, both of which are utilized in large quantities in Northwest Europe, where Brent blend crude oil is most often refined. Brent Blend production, much like that of WTI, is also on the decline, but it remains a major benchmark for other crude oils in Europe or Africa. Brent Blend oil price is often priced at a $4 higher per barrel compared to the OPEC Basket price.

**OPEC Basket** oil is a collective seven different crude oils from Algeria, Saudi Arabia, Indonesia, Nigeria, Dubai’, Venezuela and the Mexican Isthmus. The acronym OPEC stands for “Organization of Petroleum-Exporting Countries” which is an organization that was formed in 1960 in order to create some common policy for the production and sale of oil within its jurisdiction.

Because OPEC oil has a much higher percentage of sulfur within its natural make-up and therefore is not nearly as “sweet” as WTI or even Brent Blend and since it is also not naturally as “light” as well, the prices of OPEC oil are normally consistently lower than either Brent Blend or WTI. However, OPEC’s willingness or ability to quickly increase production when necessary makes OPEC a consistent “Major Player” in the oil industry!

oilprice.com

## Hop Variety Descriptions

,<"className":"col-flavor","targets":1>,<"className":"col-example","targets":2>,<"className":"col-short-description","targets":3>,<"className":"col-alpha-min","targets":4>,<"className":"col-alpha-max","targets":5>],»search»:<"search":"">,»dom»:» «>» data-filters=»<"product_cat":<"heading":"Categories","terms":[<"name":"Hops","slug":"hops","children":[<"name":"Aroma Hops","slug":"hops-aroma-hops">,<"name":"Bittering Hops","slug":"hops-bittering-hops">,<"name":"Dual-Purpose Hops","slug":"hops-dual-purpose-hops">]>],»class»:»»,»column»:»categories»,»search-column»:»hf_categories»>,»product_tag»:<"heading":"Tags","terms":[<"name":"Bittering","slug":"bittering">,<"name":"Candy","slug":"candy">,<"name":"Cedar","slug":"cedar">,<"name":"Citrus","slug":"citrus">,<"name":"Clean","slug":"clean">,<"name":"Disease Resistant","slug":"disease-resistant">,<"name":"Early Maturity","slug":"early-maturity">,<"name":"Earthy","slug":"earthy">,<"name":"English","slug":"english">,<"name":"Floral","slug":"floral">,<"name":"Flowery","slug":"flowery">,<"name":"Fresh","slug":"fresh">,<"name":"Fruity","slug":"fruity">,<"name":"German","slug":"german">,<"name":"Good Storage","slug":"good-storage">,<"name":"Good Storaged Storage","slug":"good-storaged-storage">,<"name":"Good Vigor","slug":"good-vigor">,<"name":"Good Yield","slug":"good-yield">,<"name":"Grapefruit","slug":"grapefruit">,<"name":"Grassy","slug":"grassy">,<"name":"Herbal","slug":"herbal">,<"name":"High Alpha","slug":"high-alpha">,<"name":"High Humulene","slug":"high-humulene">,<"name":"High Vigor","slug":"high-vigor">,<"name":"High Yield","slug":"high-yield">,<"name":"Homebrewing","slug":"homebrewing">,<"name":"Hop Clipping","slug":"hop-clipping">,<"name":"hop gardening","slug":"hop-gardening">,<"name":"hop tying","slug":"hop-tying">,<"name":"Hops","slug":"hops">,<"name":"Lemon","slug":"lemon">,<"name":"logo","slug":"logo">,<"name":"Low Alpha","slug":"low-alpha">,<"name":"Low Beta","slug":"low-beta">,<"name":"Medium Yield","slug":"medium-yield">,<"name":"Mild","slug":"mild">,<"name":"Mint","slug":"mint">,<"name":"Moderate Disease Resistance","slug":"moderate-disease-resistance">,<"name":"Moderate Storage Stability","slug":"moderate-storage-stability">,<"name":"Moderate Yield","slug":"moderate-yield">,<"name":"Noble","slug":"noble">,<"name":"Ornamental","slug":"ornamental">,<"name":"Passion Fruit","slug":"passion-fruit">,<"name":"Peppery","slug":"peppery">,<"name":"Pine","slug":"pine">,<"name":"Pleasant","slug":"pleasant">,<"name":"Resiny","slug":"resiny">,<"name":"Spicy","slug":"spicy">,<"name":"Stonefruit","slug":"stonefruit">,<"name":"Subtle","slug":"subtle">,<"name":"T-shirt","slug":"t-shirt">,<"name":"Traditional","slug":"traditional">,<"name":"Tropical","slug":"tropical">,<"name":"vines","slug":"vines">,<"name":"Wheat","slug":"wheat">,<"name":"Woody","slug":"woody">],»class»:»»,»column»:»tags»,»search-column»:»hf_tags»>>» data-order='[[0, «asc»]]’>A flowery, grapefruit-like aroma with medium bittering value that is gaining acceptance as a substitute for Cascade due to its citrus nature.

Flowers, citrus & spice with notes of grapefruit create the wonderful bouquet of Cascade hops. Homebrewer’s #1 hop.

Flowers and citrus are the most evident aromas. It has a medium aroma with mid to high bittering value. Often times referred to as Super Cascade.

Citra is a high alpha Hallertauer hybrid. This hop imparts interesting citrus and tropical fruit characters to beer.

A delicate blend of spices and flowers with a low bittering value.

CTZ stands for Columbus, Tomahawk, and Zeus. High on the bittering scale yet also valued for its oil content. An interesting dichotomy of sharp and herbal.

Fuggle hops offer a classic English aroma with a moderate bittering value. Fuggle hops offer pleasant wood and fruit tones which will have you heading off to the hunt.

Golding is an old school English aroma hop with flowery notes that have produced some of England’s best bitters.

Hop hash is mainly lupulin that shakes out of the dried hop cones as they head up a conveyor belt to the baler. A blend of about 10 varieties.

Aged low alpha hops.

Prized for its high bittering value. The aromatic nature is one of spice and citrus.

Simcoe’s daughter with earthy, grassy, herbal, citrus, cedar, tropical, spice and stonefruit notes adding to the pine-based pungency. A complex modern gal!

Mt. Hood is a hybrid of Hallertau with similar mild flower/spice aroma characteristics with a hint more of the forest. “Clean” commonly describes it.

A plucky American filly found herself an affable English suitor and the happy union was this well-adapted hop with its neutral, clean aroma and slightly higher-than-average bittering value. Dual purpose.

Nugget was introduced in 1970 via the USDA. It has a strong herbal/slight spice aroma and high bittering value.

Perle is a palate-pleaser with its moderate, clean bittering qualities and refreshing, spicy aroma.

Saaz is the Old World steadfast standby made famous by Pilsner Urquell. It possesses the aromatic blend of earth and spice notable in European pilsners.

Simcoe is a patented variety that is quickly finding its way into the hearts of bitter-loving craft brewers. Intense pine aroma adds to the fresh, youthful vigor.

A new variety released in 2016 by the USDA Hop Breeding program in Corvallis, OR.

A triploid hybrid of the English Fuggle hop released in 1976 from the USDA breeding program. Fragrant, spicy, woody aroma.

Name | Flavor | Example | Summary | Alpha Min | Alpha Max | hf:categories | hf:tags |
---|---|---|---|---|---|---|---|

Amarillo® Hops VGXP01 cv. | Amarillo hops have a flowery, citrus-like aroma with medium bittering value that is gaining acceptance as a substitute for Cascade due to its hardy nature. | Ales, IPAs | 7 | 11 | hops-dual-purpose-hops hops | citrus flowery | |

Cascade Hops | Very successful and well-established American aroma hop developed by Oregon State University’s breeding program in 1956 from Fuggle and Serebrianker (a Russian variety), but not released for cultivation until 1972. It has a flowery and spicy, citrus-like quality with a slight grapefruit characteristic. One of the «Three Cs» along with Centennial and Columbus. Substitutes: Centennial and Columbus (but they have a higher Alpha Acid content). | Pale Ales, IPAs, Porters | 4.5 | 7 | hops-aroma-hops hops | citrus flowery grapefruit spicy | |

Centennial Hops | American aroma-type variety bred in 1974 and released in September 1990 by S.T. Kenny and C.E. Zimmermann, the breeders of this variety. Similar to Cascade and Chinook. The genetic composition is 3/4 Brewers Gold, 3/32 Fuggle, 1/6 East kent Golding, 1/32 Bavarian and 1/16 Unknown. One of the «Three Cs» along with Cascade and Columbus. Centennial is often referred to as a ‘Super Cascade’, since it has a strong citrus aroma. | Ales, IPAs | 9.5 | 11.5 | hops-dual-purpose-hops hops | citrus flowery | |

Citra Hops HBC 394 cv. | Citra Brand is a registered trademark used with HBC 394 cv special aroma hop variety developed by the Hop Breeding Company (a joint venture between John I. Haas, Inc. and Select Botanicals Group, LLC). It was released in 2007. Citra Brand hops have fairly high alpha acids and total oil contents with a low percentage of cohumulone content. Citra Brand hops imparts interesting citrus and tropical fruit characters to beer. | 12 | 16 | hops-aroma-hops hops-dual-purpose-hops hops | citrus high-alpha tropical | ||

Crystal Hops | An American triploid variety developed in 1993 from Hallertau, Cascade, Brewer’s Gold and Early Green. It is spicier than Hallertau (cinnamon, black pepper, and nutmeg). Substitutes: any Hallertau variety, Mount Hood, Liberty. | German-style Pilsner, Lager, Kölsch, ESB, Belgian Ales | 3.5 | 6.2 | hops-aroma-hops hops | floral spicy | |

CTZ Hops | Columbus hops rank high on the bittering scale, yet are also valued for its oil content which creates a hop that is an interesting dichotomy of sharp and herbal. | American IPAs & Pale Ales, Stout, Lager | 14 | 17 | hops-bittering-hops hops-dual-purpose-hops hops | ||

Fuggle Hops | This variety was noticed growing «wild» in the hop garden of George Stace Moore’s house at Horsmonden in Kent, England in 1861. In 1875 it was introduced by Richard Fuggle who lived in the village of Brenchley (not far from Horsmonden) and hence it was called Fuggle. The aroma is earthier and less sweet than Kent Goldings. | English-style beers (particularly Stout), American Ales | 4 | 5.5 | hops-aroma-hops hops | fruity woody | |

Golding Hops | Flowery tones that have produced some of England’s best bitters. | All English-style beers (Ales, ESB, Bitter), Belgian-style Ales | 4 | 6 | hops-aroma-hops hops | english floral | |

Hop Hash | hops-aroma-hops hops-bittering-hops hops-dual-purpose-hops hops | ||||||

Lambic Hops | Belgian hop cultivated in the Aalst-Asse area near Brussels in the nineteenth and first half of the twentieth century. Because of the low bitterness the Coigneau was originally a favorite hop used for Lambic beer. | Lambics | 1 | 2 | hops-aroma-hops hops | floral fruity low-alpha | |

Magnum Hops | A high alpha acid bittering hop with mild flavor and low aromatic characteristics. | Ales, Lagers, IPAs | 12 | 15 | hops-bittering-hops hops | citrus german spicy | |

Mosaic® Hops HBC 369 cv. | Mosaic™ Brand HBC 369 cv is a daughter of the YCR 14 cv hop variety and a Nugget derived male. It has high alpha acids and tropical, blueberry, tangerine, floral, and earthy aromas. | Brown Ales, IPAs, Pale Ales | hops-aroma-hops hops-bittering-hops hops-dual-purpose-hops hops | cedar citrus earthy grassy herbal spicy stonefruit tropical | |||

Mt. Hood Hops | Mt. Hood rhizome is a Hallertauer triploid hybrid with good yield, good vigor. Mt. Hood is a half-sister to Ultra, Liberty & Crystal. | Lagers, Pilsners, Bocks, Wheat, Alt, and Helles beers | 4 | 7 | hops-dual-purpose-hops hops | clean floral pine spicy | |

Northern Brewer Hops | Grown in Europe and America as a dual-purpose hop, but mainly used for bittering in combination with other hops. Woody/earthy/fruity aroma and flavor. | IPA, Pale Ale, Hefeweizen | hops-bittering-hops hops | earthy fruity mint pine woody | |||

Nugget Hops | Floral, resiny aroma and flavor. Primarily a bittering hop. | Ales, Stouts | 12 | 14 | hops-bittering-hops hops | floral good-storage herbal mild resiny | |

Perle Hops | German dual-purpose hop. Often used in combination with other hops. Spicy and slightly floral/fruity. | Hefeweizens, Strong Ales, Lagers, Pilsners, Kolsch | 7 | 9.5 | hops-dual-purpose-hops hops | floral fruity spicy | |

Saaz Hops | An aromatic blend of earth and spice with a low bittering value. | European Noble Ales | 4.5 | hops-aroma-hops hops | earthy spicy | ||

Simcoe Hops YCR-14cv. | In 2000, Select Botanicals Group released the Simcoe Brand YCR 14 hop variety which is an aroma variety known for its versatility and unique characteristics. Simcoe Brand hops boasts several different aromas including passion fruit, pine, earthy, and citrus, and also has strong bittering qualities with an alpha acid level of 12%-14%. It is used extensively in the craft and home brewing industry. | Pale Ales, IPAs, Red Ales, Strong Ales | 12 | 15 | hops-bittering-hops hops-dual-purpose-hops hops | citrus earthy fresh passion-fruit pine | |

Triumph Hops | Not much is available regarding the flavor profile at this time. | hops | |||||

Willamette Hops | The king of aroma hops in the U.S. with its modest bittering value and sublime blend of flowers, fruit, earth and spice notes. | Ales, Lagers | 4 | 6 | hops-aroma-hops hops |

Hops can be divided into three categories: aroma hops, bitter hops, and dual-purpose hops.

**Aroma hops**have a lower alpha acid percentage and an oil profile associated with good aroma. These hops are generally used as a finishing or conditioning hop.**Bitter hops**have a higher alpha acid percentage. These hops are generally used in the boiling process to extract bitterness.**Dual-purpose hops,**such as Northern Brewer, have the qualities of both aroma hops and bitter hops, and are both aromatic and bittering.

For a more detailed description of all U.S. hop varieties, go to USDA Hop Descriptions.

© Freshops. All Rights Reserved.

Main: (541) 929-2736 · Toll-free: (800) 460-6925 · Fax: (541) 929-2702

36180 Kings Valley Hwy. Philomath, OR 97370 · Email

freshops.com

## 26 Different Types of Mathematics

Mathematics, to put it simply, is the study of numbers. But it is not merely numbers. Mathematics also involves structure, space, and change. Mathematics can be studied as its own discipline or can be applied to other field of studies.

Applied mathematics is those which are used in other sciences such as engineering, physics, chemistry, medicine, even social sciences, etc. Pure mathematics on the other hand is the theoretical study of the subject, and practical applications are discovered through its study.

Table of Contents

## 26 Types of Math

The word mathematics was coined by the Pythagoreans in the 6th century from the Greek word μάθημα (mathema), which means “subject of instruction.” There are many different types of mathematics based on their focus of study. Here are some of them:

### 1. Algebra

Algebra is a broad division of mathematics. Algebra uses variable (letters) and other mathematical symbols to represent numbers in equations. It is basically completing and balancing the parts on the two sides of the equation.

It can be considered as the unifying type of all the fields in mathematics. Algebra’s concept first appeared in an Arabic book which has a title that roughly translates to ‘the science of restoring of what is missing and equating like with like.’ The word came from Arabic which means completion of missing parts.

### 2. Geometry

The word geometry comes from the Greek words ‘gē’ meaning ‘Earth’ and ‘metria’ meaning ‘measure’. It is the mathematics concerned with questions of shape, size, positions, and properties of space.

It also studies the relationship and properties of set of points. It involves the lines, angles, shapes, and spaces formed.

### 3. Trigonometry

Trigonometry comes from the Greek words ‘trigōnon’ which means ‘triangle’ and ‘metria’ which means ‘measure’. As its name suggests, it is the study the sides and angles, and their relationship in triangles.

Some real life applications of trigonometry are navigation, astronomy, oceanography, and architecture.

### 4. Calculus

Calculus is an advanced branch of mathematics concerned in finding and properties of derivatives and integrals of functions. It is the study of rates of change and deals with finding lengths, areas, and volumes.

Calculus is used by engineers, economists, scientists such as space scientists, etc.

### 5. Linear Algebra

Linear algebra is a branch of mathematics and a subfield of algebra. It studies lines, planes, and subspaces. It is concerned with vector spaces and linear mappings between those spaces.

This branch of mathematics is used in chemistry, cryptography, geometry, linear programming, sociology, the Fibonacci numbers, etc.

### 6. Combinatorics

The name combinatorics might sound complicated, but combinatorics is just different methods of counting. The word was derived from the word ‘combination’, therefore in is used to combine objects following rules of arranging those objects.

There are two combinatorics categories: enumeration and graph theory. Permutation, an arrangement where order matters, is often used in both of the categories.

### 7. Differential Equations

As the name suggest, differential equations are not really a branch of mathematics, rather a type of equation. It is any equation that contains either ordinary derivatives or partial derivatives.

The equations define the relationship between the function, which represents physical quantities, and the derivatives, which represents the rates of change.

### 8. Real Analysis

Real analysis is also called the theory of functions of a real variable. It is concerned with the axioms dealing with real numbers and real-valued functions of a real-variable.

It is pure mathematics, and is good for people who like plane geometry and proving.

### 9. Complex Analysis

Complex analysis is also called the theory of functions of a complex variable. It deals with complex numbers and their derivatives, manipulation, and other properties. Complex analysis is applied in electrical engineering, when launching satellite, etc.

### 10. Abstract Algebra

Sometimes called modern algebra, abstract algebra is an advanced field in algebra concerning the extension of algebraic concepts such as real number systems, complex numbers, matrices, and vector spaces.

One application of abstract algebra is cryptography; elliptic curve cryptography involves a lot of algebraic number theory and the likes.

### 11. Topology

Topology is a type of geometry developed in the 19th century. Its name’s Greek origin, which is ‘topos’, means place. Unlike the other types of geometry, it is not concerned with the exact dimensions, shapes, and sizes of a region.

It studies the physical space a surface unaffected by distortion contiguity, order, and position. Topology is applied in the study of the structure of the universe and in designing robots.

### 12. Number Theory

Number theory, or higher arithmetic, is the study of positive integers, their relationships, and properties. It is sometimes referred to as “The Queen of Mathematics” because of its foundational function in the subject.

### 13. Logic

Logic is the discipline in mathematics that studies formal languages, formal reasoning, the nature of mathematical proof, probability of mathematical statements, computability, and other aspects of the foundations of mathematics.

It aims to eliminate any confusion that can be caused by the vagueness of the natural language.

### 14. Probability

Probability is the branch of mathematics calculating the chances of some things to take place based on the number of the possible cases to the whole number of cases possible. Numbers from 0-1 are used to express the chances of something to occur.

0 means it can never happen and 1 means it will always happen. Real-life applications are in gambling, lottery, sports analysis, games, weather forecasting, etc.

### 15. Statistics

Statistics are the collection, analysis, measurement, interpretation, presentation and summarization of data. Statistics is used in many fields such as business analytics, demography, epidemiology, population ecology, etc.

### 16. Game Theory

Game theory is a branch of mathematics which also involves psychology, economics, contract theory, and sociology. It analyses strategies for dealing with competitive strategies where the outcome also depends on other actions of other partaker in the activity.

It is applied in business, wars, political sciences, biology, philosophy, etc.

### 17. Functional Analysis

Functional analysis is under the field of mathematical analysis. Its foundation is the study of vector spaces that has limit-related structure such as topology, inner product, norm, etc.

It was developed through the study of functions and the formulation of properties of transformation. Functional analysis is found to be useful for differential and integral equations.

### 18. Algebraic Geometry

Algebraic geometry is a branch of mathematics that uses algebraic expressions to describe geometric properties of structures.

### 19. Differential Geometry

Differential geometry is a field in mathematics that utilizes different mathematical techniques (differential calculus, integral calculus, linear algebra, and multilinear algebra) to study geometric problems.

It is used in different studies of electromagnetism, econometrics, geometric modeling, digital signal processing in engineering, study of geological structures.

### 20. Dynamical Systems (Chaos Theory)

Dynamical Systems (also referred to as chaos theory) is a mathematical concept where the relationship of a point in space to time is described a fixed set of rules. This concept explains the swinging of a clock pendulum, flow of water in a pie, number of fishes in a lake during springtime, etc.

### 21. Numerical Analysis

Numerical analysis is an area in mathematics which develops, evaluates, and applies algorithms for numerically solving problems that occur throughout the natural sciences, social sciences, medicine, engineering and business.

### 22. Set Theory

Set theory is a discipline in mathematics that is concerned with the formal properties of a well-defined set of objects as units (regardless of the nature of each element) and using set as a means of expression of other branch of math.

Every object in the set has something similar or follows a rule, and they are called the elements.

### 23. Category Theory

Category theory is a formalism that is used for representing and manipulating concepts and symbolic representations of domains. Here, the collection of objects and of arrows formalizes mathematical structure.

### 24. Model Theory

Model theory in mathematics is the study of different structures from a logical standpoint. It involves interpretation of formal and natural languages and the kinds of classifications they can make.

### 25. Mathematical Physics

Mathematics as mentioned earlier is used in many different other fields. Physics is just one of them. Mathematical physics refers to the mathematical methods applied for different studies and development in physics.

### 26. Discrete Mathematics

Unlike the many other ones mentioned above, discrete mathematics is not a branch, but a description of the study of mathematical structures that are discrete rather than continuous.

Discrete objects, in simple languages, are the countable objects such as integers. Therefore, discrete mathematics does not include calculus and analysis.

differenttypes.net