Windows over the bathtub should placed. A window behind the toilet is seldom desirable. Skylights may be used to serve top-floor bathrooms if they are quate light large enough to provide adeand ventilation. Inside bath-. For guest baths or toilets, space is needed only for dentifrices, shaving accessories, toilet preparations, and a few simple remedies.
Floor space should be left in every bathroom for portable accessories desired by the owner or needed on occasion for the care of infants or invalids. Also consider allowing stool table 4 or ft or of space seat, floor for such infant's space in items as scales, bath and dressing use , and soiled-linen table ultra-violet. For each person regularly using the bathroom, thera should be separate bar space for bath towel, face towel, and face cloth, as well as an additional rack for guest towels.
Linen storage may consist of towel cabinets recessed in the thickness of plumbing walls either over fixtures or as full height cabinets or may be expanded into complete linen closets.
Dressing-rcom baths may include completely fitted wardrobes. See Table 3. Minimum-sized require special bathrooms planning to and ensure toilets ade-. Department of Agriculture, Washington, D. An accurate list of the objects to be stored is necessary for the scientific allotment and arrangement of space and facilities. A "margin of safety" of some 25 per cent increased capacity should be allowed for the usual accumulation of additional belongings.
It is better to have too much space than not enough. Much can be stored in little space if sufficient thought is given to the arrangement of the space and the equipment. Too many closets have unused and unusable space due to poor planning. Good closet design requires planning, arrangement, and fixtures contributing to : 1. Convenience a. Ease of access b. Maximum visibility c. Orderliness d. Maximum accessibility e. Maximum of used space 2. Preservation a. Of pressed condition b.
Of freshness ventilation c. From moths d. From dust e. From pilfering The above are not all simultaneously obtainable, and some are mutually exclusive; for instance, eliminating doors gives maximum availability but minimum security from dust, moths, and pilfering ; adhering to the principle of maximum accessibility would result in unused space at top and bottom of closet.
Alternate closet closing methods may involve more complicated or more expensive construction, though they may obviate the objection that swinging doors form an obstruction in the room. Sliding doors can expose the entire interior of the closet to view and make it immediately accessible. Such doors do not block traffic. Sliding doors, however, do not permit the use of special door fixtures such as tie racks, shoe racks or bags, hat hangers, or mirrors, which are handy and easily reached when attached to a hinged closet door.
Banks of wardrobe-type closets with sliding doors are becoming more and more popular. Fitted with drawers or trays, they take the place of bureaus, chests, and chiffoniers and make far more spacious, uncluttered rooms. Doors which expose the full width of the closet are preferable for both visibility and accessibility.
Some of the various closing methods are shown in Fig. Lighting is considered essential and standard in the modern closet unless room lights are located to illuminate fully all portions of the closet.
A single tubular or bulb light with a diffusing reflector placed just above the door inside the front of the closet is usually sufficient. Automatic door switches are convenient. Ventilation is often desirable, particularly in hall closets where damp outer garments or work clothes might be stored. It can be accomplished readily by providing louvers in the closet door or by using louver doors.
Types of closets Closets are required for various purposes, in different parts of the house. Some have already been mentioned in other sections of this volume : kitchen supplies ; dinnerware, glassware, and table linens discussed under "Kitchens" ; and bathroom supplies discussed under "Bathrooms". Closets must also be provided for the storage of clothing, bedding, cleaning equipment, books, magazines, and phonograph records, toys and other children's and adults' recreation equipment, and certain items such as luggage that are used only seasonally or infrequently.
The discussion here relates only to "active" storage space. Clothes closet. For clothes closets in bedrooms or dressing rooms, 2 ft is standard depth 2 ft 6 in. This permits clothing to be on hangers on poles, with sufficient clearance. Clothing lengths are shown in Fig. Clothes closet width, parallel to the doors, should be from 3 to 6 ft per person, depending on amounts of clothing and.
Modern closets, by the efficient arrangement of space and fixtures, accommodate much more clothing and material than the inconvenient, space-wasting closets of a few decades ago. The modern closet often replaces pieces of furniture and thus provides a greater amount of free, uncluttered space in the room. Doors should open the full width of the closet whenever possible.
In most cases the most efficient and economical doors are the usual hinged type. Two doors for a 5-ft closet will eliminate dark, inaccessible, hard-to-clean corners. Hooks, racks, and accessories on the backs of swinging doors increase efficiency by using otherwise unoccupied space in the closet. Some typical closet plans are illustrated in Fig.
Coat closets, doors, the are and children are shown entrance or 3 in. Several designs for coat closets are shown in Figs. Closet for cleaning equipment : The dimensions of the storage space needed for cleaning equipment will depend in large part upon the type used ; horizontal, ommended shown in Fig.
The closet should be located as near the center of the house as possible, and should be FHAI requirements for linen closets are as follows : minimum interior dimensions, 18 in. A suggested design for a cleaning equipment closet is shown in Fig. Storage for bedroom linens and bedding : Limited and liberal lists of articles of bedding that require storage, and the minimum dimensions of the space required, are shown in Table 1.
These are minimum dimensions, and about twice this amount is recommended, espe cially if both bedroom and bathroom linen are to be stored. A suggested layout for such a combined Fig. A minimum size closet of a usual type. Shoes can be stored on the raised shelfrack and three additional pair on the floor in front of the rack.
Door could be arranged for hats as shown below, Heaving shelf for other storage. Minimal closet arranged to make shoes more visible and reachable. There is space for hats without crushing or for night clothes hooks if hats are normally stored in a hall closet. Neckties might be in two tiers. An alternate to the scheme above giving maximum view of shoes and an additional shelf.
Trousers would have to be folded over the crossbar of the suit hanger rather than being hung separately from the pole with trouser-hangers. Bedroom closets for men. A four-foot closet with seven drawers for shirts, socks, underwear, etc. Night clothes and bathrobe hooks are best on the right band door, necktie racks flat against the Heft hand door.
Another four-foot closet with ten standard drawers conveniently arranged. Shoes are placed tandem above the drawers for visibility and reachability. Poles are one above the other, requiring reaching. A solution to the shallow closet problem. A pull-out rod takes care of the suit, coat and trouser hanging. Five drawers take the place of a small bureau or chest. Shoes are at "no stoop, no squat, no squint" levels. Wide wardrobe closets of more luxurious size planned as part of walls separating two rooms.
Four doors, sliding or swinging, can be used. Lower portion of shoetiers could be replaced with mothproof "dead-storage" drawers. A deep walk-in closet. High tiers of shoe racks flank the door jambs. Shelves for Hive and dead storage on three sides, upper levels.
Suit poles range the back wall. Ties are on the left wall, night clothes hooks on right wall. A small closet with shoe racks at the side under short hanging garments. Additional shoe pockets might be placed on the door under the hanging shelves. These handy shelves fold into the space in front of the hat and storage shelves.
An alternate minimum closet arrangment with a high pole for Hong dresses. Two drawers below the shorter hanging garments. Depth of closet permits a door type shoe rack and a hat rack. Wide bats can go on upper shelf. Alternate to closet above. It provides a high pole for banging evening dresses and a lower pole for other dresses and suits.
A large hat shelf is provided above the low pole as well as a hat rack and shoe pockets on the door. Bedroom closets for women. A four-foot closet combining hanging and shelf space with drawers for stockings, underthings, and what-not.
Shoes are easily seen and chosen from the almost eye-level cleat rack above the drawers. Hat storage on the shelves. Another four-foot closet with a short cantilever pole at the left allowing two-decker hanging.
Closet drawer space would naturally be supplemented by a bureau or other furniture. A shoe rack on the door would increase capacity. The shallow closet problem solved by the use of a pull-out rod firmly anchored to the back wall.
Drawers again at lower right with cleated shoe shelves above, and hat shelves above them. Drawers may have to be shorter than standard. Large double wardrobe type closet, almost half devoted to hanging space.
Left half fitted with large and small drawers and wide shelf-counter with mirror above. Sliding doors may be preferred and center partition minimized. A walk-in closet, shoe racks and shallow shelves at one side drawers and hanging pole at the other. Drawers next to door are convenient but hazardous if Heft open.
They could be placed at the back with hanging space near door. Closet for infants up to about 5 years old, LOW hanging pole shelves and drawers permit habits of care and orderliness to be developed at an early age. Note two sets of doors,. Small closet designed for a child of from 6 to 10 years. Pole at higher but easily reached level. Drawers and shoe racks convenient heights. Ample shelf room at provided above for the storage of possessions.
Alternate, and larger, closet for an infant up to 5 years of age. Trays or drawers for folded garments at an upper level for adult use. Hanging space, drawers and shelt available to child using the lower doors. Bedroom closets for children. Closet for youngster up to 10 years old, providing greater length of hanging pole and different shoe arrangement, trays instead of cleat racks. A large shelf for hats, toys. Included in this category are books, magazines, phonograph records, card tables and chairs, games, movie and slide projectors, screens and film, toys, sports equipment,.
If adequate and conveniently located built-in storage is not provided, then portable units furniture will have to be used for this purpose. Book storage is usually required in the living room, study, and each bedroom. Most books 85 per cent can fit comfortably on shelves 8 in. Vertical spacing between shelves varies from 8 to 16 in. Horizontally, books average 7 to 8 volumes per linear foot of shelf. Phonograph records 12 in. Card tables are usually 30 in.
Folded chairs vary widely in dimension, but a fair average is 30 by 16 by 3 in. Space should also be provided for cards, score cards,. Sports equipment, especially golf bags, skis, and camping equipment, may present a serious storage problem.
For some families, a separate closet for this purpose may be justified ; a suggested design is shown in Fig. Such a closet should be located near the outside entrance which is most used by the family. Tools and associated items should, of course, be stored in the workshop, which every house must have. Paints, because of odor and fire hazard, are best stored outside the house.
General storage is required for bulky, seldom-used items, such as trunks, boxes, and extra furniture. Outdoor storage i. Toy and game storage should be provided in children's bedrooms and wherever the toys are regularly used. Toy storage should be designed for future conversion to other use.
These last two types of storage general and outdoor were provided in the traditional house by the basement, attic, and garage. Modern houses may have none of these spaces, and, in such cases, the architect should take particular care to provide adequate general and outdoor storage space. FHA minimum requirements are cu ft plus 75 cu ft per bedroom, of which at least 25 per cent and not more than 50 per cent should be indoors.
Again, it should be emphasized that this is a minimum requirement; more is recommended. Basic elements The standard elements of closet storage are shelves, drawers, poles, hooks, and. Practically any object can be stored efficiently by one or another of these means.
The choice and arrangement of the fixtures depend on the amount and nature of the materials to be stored. Shelves : Shelves are simple and inexpensive to install, require a minimum of effort to use, and are adaptable to the storage of many types of things, especially those of odd or bulky shape, folded articles, and, of course, books, magazines, etc.
However, if open, they are exposed to dust. Also small objects become hidden behind one another if the shelves are deep. A in. Articles of larger dimensions or greater depth should have their special places ; linens, for instance, are frequently folded for a in. Drawers are growing in popularity in closet design because they accommodate numerous articles with a minimum of.
A recent logical outcome of this situation has been the development of molded plastic drawers in a variety of stock sizes. Fronts of various materials can be attached. All that is required of the builder is the construction of the supporting enclosure.
Hanging pole length can be estimated roughly at 3 in. Height of pole above floor should average 64 in. They provide practically dust-free storage and present a neat appearance even when carelessly used.
Drawers of different widths and depths make possible classified "filing" of different items, thus providing a great saving in time and an incentive to orderliness.
A cabinet made up of a battery of standard drawers, selected for the storage of the known possessions of the user, can easily be made from a comprehensive list, with allowance made for the accumulation. Drawer construction is cabinetwork requiring both skillful craftsmanship and the best materials.
They must operate freely under all seasonal and climatic conditions. Clearance between pole and shelf above should be 3 in.
Hardwood poles 1 in. Consult manufacturers for special-purpose hanging rods, extension poles, brackets, etc. Hooks : A variety of hooks is available. Special features ; Such special features as shoe and hat racks and miscellaneous racks are on the market and greatly increase convenience in storage.
This need for new housing, considered against a background of continuing urbanization, clearly indicates that an increasing proportion of an expanding housing market will be devoted to multifamily types of housing or apartments. The inevitability of this trend contains a challenge to the architect to do more then merely meet a statistical demand. He must rather address, identify, and solve the problems of multifamily building types as an attractive alternative to freestanding singlefamily buildings.
This article will deal with multifamily living in general, with some additional attention to the problems of the medium- and high-rise building type i. This article will be developed in the same sequence as Table 1. It must be borne in mind that, as with any design development, the evolution of an apartment building design is not a sequential process but a process of continuing interaction, feedback, and reevaluation, and that the number and complexity of events will vary according to the program, scope, and funding sources involved.
The sequences shown are labeled as program development, site analysis, building planning, and building design. Program development is for the most pert evaluation of information over which the architect has relatively little control but which shapes the project in a basic way.
Site analysis involves evaluation of physical data which must be recognized, identified, and weighed by the architect in making basic design decisions dealing with site use, allocation, and development.
PROGRAM Market Analysis A market analysis and program formulation may precede the retention of an architect ; however, to an increasing degree clients solicit the aid of an architect in these areas. An investigation of the potential market should consider existing market conditions and trends with regard to 1. Type of occupancy a. Rental b. Cooperative c. Condominium 2. Price rent, maintenance, etc.
Amenities 4. Apartment size area and number of rooms. Building types 6. Vacancy rates 7. Public facilities transportation, schools, shopping, recreation Program items to be resolved include Price range. What segment of the market is the project to be aimed at? Identified in Table 2 as support facilities and closely interrelated with price range. How many units?
Percentage of each type of unit. Building type or types. Funding in many cases a market analysis will conclude that conventional private financing is not economically feasible and that some type of public or semipublic assistance is required if a project is to proceed. There are a number of sources of such assistance at both federal and state levels.
As a rule, an agency which provides assistance also requires conformance to agency standards, and frequently such an agency will require approval of or participation in program development. While the client, local authorities, and funding sources will usually institute basic program direction, it nevertheless remains the responsibility of the architect to catalyze these decisions and formulate the finished program.
Density Figure t compares relative densities of various urban and suburban situations. It is helpful to "have a feel" for the physical reality of density figures as an aid in visualizing possible solutions and to anticipate implications of decisions which are made during program formulation. Appropriate local and regional authorities should be contacted in order to determine the type and extent of limitations or controls which may be imposed on a project and, further, to gauge the discretionary powers and flexibility of the governing authorities.
To an increasing degree, the philosophy of zoning is changing from one of restrictive limits and controls to an approach which attempts to lead and influence community growth. Many communities and regional authorities have guiding master plans which deal with long-range development and evaluation. The conceptual and planning freedom of the architect is linked with these considerations. Failure to pursue a thorough investigation of these controls can result in serious problems later on in project development.
Controls Zoning is concerned principally with questions of use, bulk, density, and location. Use, bulk, and density are usually controlled. Uses may be designated as, for example, residential, commercial, manufacturing, and, in some cases, park or recreational. Mixed uses are frequently allowed, end for large housing projects it is considered advantageous to incorporate retail shopping, entertainment, and dining facilities into a program. Location of buildings is controlled in order to prevent oppressive proximity of building masses.
See Figs. Density regulations limit the number of people per site-area unit. The basis for density determination will vary from regulation to regulation. Density may range from a low of ten or fewer people per acre in low-density districts to a high of up to 1, or more per acre in the highest-density districts.
Borings and samples taken at the site will provide information regarding location and extent of rock, bearing capacity of the subsurface strata at various levels, and the level of a water table.
A survey indicating boundaries, contours, or spot elevations is necessary and, in the case of difficult sites, such a survey may indicate terrain and other conditions which will strongly influence design decisions.
Limitations imposed by difficult terrain-in addition to those imposed by local laws or ordinancesmay limit such items as location of driveways and parking entrances. Site Elements Figure 5 diagrams possible relationships among site layout elements which normally occur in apartment development. As suggested by the diagram, it is desirable to limit cross traffic among circulation elements such as vehicular access and pedestrian access and to maintain proximity or easy access among activity elements such as the dwelling unit, recreation, and parking.
The relationships may be horizontally or vertically arranged, depending on density or tightness of a site. Emphasis on the importance of certain relationships may vary with the program ; however, the basic elements and relationships remain. Figure 6 shows examples of different arrangements of the site elements-arrangements which reflect program density relative to site area.
Building Access Figure 7 diagrams various means of building access and internal circulation, each with different advantages and degrees of suitability to specific design solutions.
Utilities Availability, adequacy, and location of site utilities enter into basic decision making. Bulk is frequently controlled by floor-area ratio, which limits total buildable floor area as a multiple of the site area. In contemporary zoning regulations, floor-area ratio for apartment buildings will range from a low of 1 or less to a high in the range of 14 to 16 in dense metropolitan areas.
Building codes are less regional and vary less than zoning regulations. Many localities adopt national or state building codes as their standard. Such codes are concerned with health and safety requirements such as light and air, access, egress, construction standards, minimum dimensional standards, fire detection and protection, and fire equipment access. Inadequacy or unavailability of certain services may require on-site generation or disposal facilities.
Building Orientation Building orientation may be influenced by a number of factors such as site, view desirable or undesirable , sun, and prevailing winds. Closely interrelated to building orientation is the question of internal circulation and floor layout of the building.
Figure 8 indicates how different layouts lend themselves to solutions of site problems. Standards Similar to zoning and codes and equally important in many cases are governmental agency standards, which apply when public or semipublic funding sources are involved or mortgage standards if private funding is involved. The need for a thorough initial investigation and continuing review for conformance with controls imposed by zoning, codes and agencies cannot be overemphasized.
Large Scale Large-scale residential developments involve special problems and opportunities. Closing or rerouting of streets wholly within a project is frequently undertaken and can free up area, eliminate restrictions of a street grid pattern, and generally change the scale and feeling of a project. When through streets within a project are closed or otherwise restricted, compensatory widening and improvement of peripheral roads is usually in order not only to offset the effect of the closings but also to accommodate the increased traffic flow generated by the project itself.
Similarly, shutting down a utility line and adding to demand generally requires compensatory improvement.
The shape of the repetitive typical floors influences the cost of constructing and enclosing the floors. For purposes of economy and efficiency, building shape should be such that expensive exterior walls are minie,ired in.
Area of a typical floor may affect costs. For example, pouring of a typical tier in a castin-place concrete building is a continuous process and requires a full concrete crew throughout. The area of a typical floor or part thereof should be such as to efficiently utilize the day's productivity of a concrete crew. Similar analysis and considerations should be applied to other building techniques or systems. Building Height The cost of a building may be affected by building height.
A building may be of such height that it exceeds prevailing capacities in terms of available construction equipment and contractor experience. In addition to considerations of what is possible, there are considerations of what is practical and efficient from a cost standpoint.
Of the various mechanical systems which serve an apartment building, each has various increments and "stepup" points. For example, there is a situation such that the addition of a single extra floor could require a substantial increase in elevator service either through an additional elevator or an expensive increase in elevator speed.
Similar situations exist for heating, cooling, plumbing, and ventilating systems, and opinions of the various consultants in these areas should be solicited. Length and Width Additional costs resulting from an increase of building length or width are generally proportionate to increase in area, However, as with other such items, there are step-up points at which there are disproportionately large increases in cost for slight dimensional increases. Wind Bracing Wind bracing becomes a structural design consideration in buildings beyond the to 12story range, and one must then consider measures which may be introduced to resist the overturning tendency due to wind loads.
Wind bracing may be achieved by introduction of various structural measures. The extent and, therefore, the expense of these measures may be reduced if the building shape itself contributes to wind bracing.
As the diagrams Fig. This structural approach has certain advantages which make it particularly adaptable to apartment construction. The horizontal services normally required in apartment construction may be imbedded. Steel Although much less common than cast-inplace concrete, steel frame structures are also employed in the construction of apartment buildings.
The advantages of strength and relative simplicity of erection may recommend steel for use in extremely tall structures or for use in locales where there is limited experience in the use of concrete. Steel structural frames tend to be laid out in a regular grid pattern, and this in turn regu-. This reduces floor-to-floor and overall building height and eliminates the separate construction of a hung ceiling.
The possibility of placing columns randomly adapts well to the inherently irregular module generated by a typical apartment floor layout.
Columns may thus be "buried" in convenient locations within an efficient layout. As a rule, openings for vertical services may be located at will in this type of structure ; however, large openings near columns should be handled with care so as to assure continuity of vertical and horizontal reinforcing.
One should bear in mind that in this type of structure mechanical and structural lines may not coincide. Limitations As a rule of thumb, spacing between concrete columns may economically be in the range of to ft centers and spacing for steel columns may range from 16 to 24 ft.
Figure 12 may serve as a guide for sizing of concrete columns in preliminary layouts. Three common bay sizes or center-to-center distances have been shown for various building heights. Sizes are for internal columns, expressed in square inches.
Peripheral and corner columns will be smaller. The smallest dimension per side considered acceptable for concrete columns is 10 in. Columns with larger dimensions become, in effect, walls and are formed differently.
It is significant to note from the chart that an internal column in a tall building may be on the order of 2 by 3 ft. Such a planning element cannot be overlooked even for preliminary sketching. Systems Approach Any discussion of structural considerations in conjunction with housing must recognize that the housing industry appears to be at the beginning of an era of greatly increased prefabrication, which is leading towards full systems building and industrialization of the building process.
Travel distance 2. Elevator speed 3. Elevator capacity 4. Building population Travel distance is represented on the graph as "Number of stories" based on the assumption of normal floor-to-floor heights. Possible speeds for buildings of different heights are shown. Building population is represented on the graph as "population per floor," with curves shown for typical floor populations. In determining population, two persons per bedroom are assumed. Egress and Safety. Prefabrication and systems building has been applied widely in European countries for a number of years, and there have been many prototypical developments and limited applications of techniques in this field in the United States.
It is anticipated that, within the foreseeable future, virtually all European housing will be the product of some type of system. It would appear inevitable that progress toward industrialized construction will likewise continue in the United States. At what precise point the utilization of systems building will become a major consideration in apartment design and what system or systems will survive to become a standard of the future is uncertain ; however, it is a significantly growing field which will be watched closely by practitioners in the housing field.
Of the number of systems which are presently available, the following categories may be drawn : 1. Steel or concrete frame with precast planks, self-formed concrete deck or metal deck 2.
Poured-in-place concrete tiers utilizing special reusable forms for transverse walls or columns 3. Prefabricated floor-size truss or beam systems with clear span capabilities. Preassembled modules, prepared site or on site, for stacking or insertion in a structural frame Figure 13 shows a composite structure including the categories described.
Any proposal to use a building system should be preceded by a thorough investigation as to availability, code and market accepts-. Except in rare circumstances, relatively little in the realm of egress and safety is left to the discretion of the architect.
In general, the architect may choose only among accepted and approved procedures as set down in codes. In most codes, two means of egress must be provided within specified distances from each dwelling unit Fig.
Figure 1 5d diagrams a scissor stair which, as shown, is an arrangement which allows for construction of two stairs in one fire enclosure. This is an efficient and cost-saving solution to the two egress requirements. Most codes, however, effectively preclude the use of scissor stairs, in many cases by limiting the allowable length of dead-end corridors. Fire escapes are usually required for construction that is not fireproof ; and sprinklers, smoke doors, fire detectors, and alarms are additionally required for various classifications of construction in some codes.
Figure 14 may serve as a preliminary guide in determining number and type of elevators necessary for an efficient solution. Vertical plumbing risers and waste lines or "plumbing stacks" are expensive due to both material and labor costs. Reduction in the number of stacks saves money and is, therefore, to a greater or lesser extent advantageous and advisable.
Reduction in the number of plumbing stacks is accomplished by doubling or even tripling up on each stack at each floor. These dimensions, it should be remembered, are for rough layout purposes only and should be verified by consultants. Ventilation Interior spaces such as bathrooms, interior kitchens, and public halls require mechanical exhausting.
Figures 17 and 18 may be used as guides, in making preliminary layouts, to determine the floor area to be allocated to exhaust ducts. Figure 18 indicates the area of exhaust and Fig. The ratio of dimensions should be as close to square as possible and should not exceed a ratio of 3 A mechanical engineer should be consulted to determine final data regarding size and Iotation of ducts.
The most common exception is the case in which ducts deliver conditioned air from either a tentral source or a unit in the apartment. In such a case, ducts may be of such size as to become a planning factor.
Pipe risers as shown in Fig. It is desirable to avoid having a common riser between separate apartments. The principles of the pro-. Plan of story apartment building with hatched areas indicating space devoted to vertical service elements. Procedure Sequentially, the steps in the determination of a typical floor in an ideal case could proceed as follows : See also Fig. Investigate program with regard to the total number and types of apartments.
Identify repetitive groups with each group possibly representing a typical floor. Assign area figures to apartments as determined in program analysis or as required by governmental agency standards. Total up the area of the apartments in a repetitive group and to this total add 10 to 15 percent for corridors and cores. This material is protected under all copyright laws, as they currently exist.
No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. Check out the preface for a complete list of features and what's new in this edition.
Pearson offers affordable and accessible purchase options to meet the needs of your students. Connect with us to learn more. Stephen H. He was a faculty member at Illinois State University for 32 years, where he was recognized as the outstanding teacher in the College of Arts and Sciences in He has authored or coauthored articles and books in analysis and linear algebra. Arnold J. He served as a faculty member at Illinois State University for 31 years and at Illinois Wesleyan University for two years.
In addition to authoring and co-authoring articles and books in linear algebra, he has written articles in lattice theory, topology, and topological groups. Lawrence E. He served as a faculty member at Illinois State University for 34 years, where he was recognized as the outstanding teacher in the College of Arts and Sciences in He is an author or co-author of nine college mathematics textbooks, as well as articles in mathematics journals in the areas of discrete mathematics and linear algebra.
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